Acronym QRAC Proposal title Algorithmes et complexite ...magniez/qrac/uploads/Main/qrac-b.pdfThe...

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No de dossier : ANR-08-XXXX-00Date de revision :

Document de soumission B Edition 2008

Acronym QRACProposal title(in French)

Algorithmes et complexite quantiques et probabilistes

Proposal title(in English)

Quantum and Randomized Algorithms and Complexity

1 Technical and scientific description of the activities

1.1 RationaleOur project consists in joining the strengths of experts in both randomized and quantum computation. Our globalobjective is to make progress on both quantum and probabilistic computation, and also, by joining forces, to ensurethat the flow of techniques goes in both directions, from randomized computation to quantum and back.

In randomized algorithms, our emphasis is on data-intensive models with restricted data access where ran-domization and sometimes approximation are fundamental tools. The areas we will cover are Property Testing,Streaming Algorithms, Online Algorithms, and Algorithmic Game Theory.

In quantum computation, we will continue to work on algorithms, especially for the Hidden Subgroup Problemand Vector Lattice Problems, and also on Quantum Walk based algorithms, on Quantum Query Complexity lowerbounds, Complexity, Quantum Information and Communication.

At the intersection of quantum and randomized computation, our goal is to study Locally Decodable Codes,Communication Complexity, and Circuit Lower Bounds.

1.2 Background, state of the art, issues and hypothesesThe principal challenges in the design of algorithms include not only the inherent difficulty of computational tasks,as witnessed by the NP hardness of many everyday problems, but in recent years, the staggering increase in the sizeof data. Some of the most successful proposals from the randomized algorithms community include relaxing theproblems by allowing approximate results, or allowing a small probability of error in the result. Faced with massivedata sets, on-line algorithms and algorithms that query a very small portion of the input, as in the framework ofproperty testing, address these issues as they often provide good approximations for otherwise intractable problems.

Quantum computation has been put forward as another way to overcome current computational limits, by ex-ploiting the quantum properties of nature. Over the past decade, strong, steady advances have been made in un-derstanding the advantage and limitations of the model. Shor’s algorithm for factoring, and its generalization, theHidden Subgroup Problem (HSP), has been suceessfully extended from abelian to a number of non-abelian groups.The Graph Isomorphism Problem is the most important non-abelian instance of HSP, and progress towards thisquestion is a long-term goal of research in this area. Many algorithms for everyday problems have been developedharnessing quantum tools such as Grover’s search for a marked element in an unstructured list, and amplitude am-plification. Random walks have been successfully adapted to quantum computation and have been shown to bemore efficient than their classical counterparts. Communication complexity has shed light on the nature of quantuminformation and new, sophisticated techniques for proving lower bounds have emerged.

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ANR2008 - Document B / anglais

The tools from the design and analysis of randomized algorithms and protocols have been the main startingpoint for much of the work in quantum computation, for example in the case of quantum walks. But perhaps themost surprising and interesting trend in quantum computation is that the flow of techniques and results has steadilybeen going in the reverse direction as well. Improvements in classical locally decodable codes and lattice problemsresulted from quantum techniques. Lower bound techniques for query complexity has been shown to generalizemost known techniques in classical circuit complexity. These are examples in this growing trend, and the time hascome to explore these connections in a more structured way.

1.2.1 Work package A: RANDOMIZED ALGORITHMS

Randomization and also approximation are important tools in algorithmics whose number of applications increasesdramatically with the new challenges of modern computer science.

One of those challenges focuses on the way that the data (input) can be accessed. The size of the data thatalgorithms are called upon to process in everyday, real-time applications has grown considerably in recent years,for example in bioinformatics for genome decoding or in Web databases for the search of documents. Linear-time,even polynomial-time, algorithms were considered to be efficient for a long time, but this is no longer the case,as inputs are vastly too large to be read in their entirety. Sublinear algorithms, i.e. algorithms that don’t read allof their input are a possible approach to overcoming this problem. Such algorithms were pioneered by PropertyTesting. These algorithms are usually robust by definition, as they are not influenced by local errors. Robustnessis becoming crucial since massive data sets cannot be perfect as their source is often disparate and unreliable, andphysical storage devices are error prone.

Another challenge is to handle restrictive accesses to the input. Streaming algorithms and Online algorithmsfit into this setting. Streaming algorithms read their input piece by piece, are further restricted in the amount ofmemory at their disposal, and have to compute a function (or an approximation of a function) of the whole input.Online algorithms receive their input piece by piece, and have to take an irrevesible action upon receipt of eachpiece. Yet another model of restricted data access is Distributed Computing, where the input is shared betweendifferent entities. The last model we will investigate is the one used in Algorithmic Game Theory. In comparisonto the model of Distributed Computing, here each entity has his own objective that it tries to maximize.

Property Testing and Streaming Algorithms We are particularly interested in the design of sublinear algorithmsin the context of approximation. Depending on whether the studied problem is a decision problem or a function, twoprincipal notions of approximation can be defined. When an algorithm is only required to approximately computea (numerical) value, we speak about Approximation Algorithms. In the case of decision problems, the approxi-mation condition can be moved to the input as was done in Property Testing. Property Testing is a statistics basedapproximation technique to decide whether an input satisfies a given property, or is far to any input satisfying theproperty. Initiated by Manuel Blum (Turing award) in 1989, it applies to numerical analysis, functional equations,geometry, language theory, graphs and quantum computation [FMSS03]. In this approach, one looks for a compro-mise between robustness and efficiency. Inspired by the work of Blum and Kannan [BK95], and Blum, Luby andRubinfeld [BLR93], Property Testing was defined for graph properties by Goldreich, Golwasser and Ron [GGR98].Given a distance between objects, an ε–tester for a property P accepts all inputs which satisfy the property andrejects with high probability all inputs which are ε-far from inputs that satisfy the property. Inputs that are ε-closeto the property lie in a gray area where no guarantees on the result are given. These restrictions allow for sublinearalgorithms, and even constant time algorithms, whose complexity only depends on ε.

In opposition to Property Testing where the access to the input is restricted by a sublinear number of samples,Streaming Algorithms can scan sequentially the whole input only once (and not e.g., have random access to theinput), while maintaining sublinear memory space, ideally polylogarithmic in the size of the input. The area ofstreaming algorithms has experienced tremendous growth over the last decade; computing over continuous streamsof data using only a limited amount of memory has become of key importance in many applications. The design

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of streaming algorithms is motivated by the recent considerable growth of the size of the data that algorithms arecalled upon to process in everyday real-time applications, for example in bioinformatics for genome decoding, inWeb databases for the search of documents, or in network monitoring.

In the area of streaming algorithms, the analysis of the Internet traffic [AMS99] (2005 Godel Prize) was oneof the first applications, where traffic logs are queried. The main approach is to associate a sketch with a flow,as a compression of the data from which various properties can be exactly or approximately decided. Only fewapplications have been made in the context of decision problem on massive data such as DNA sequences, largeXML files. In [FKSV02], a comparison between the Property Testing and Streaming Algorithms has been made,showing some connections and differences between the models. This justifies the promising approach of StreamingAlgorithms when Property Testing fails. Another advantage of Streaming Algorithms is that it does not alwaysrequire an approximation of the input, whereas this is a requirement of Property Testing.

Online Algorithms The area of online algorithms has become an established field in theoretical computer science.It deals with the design and analysis of algorithms that operate in a state of incomplete information, usually dueto the lack of information about the future. Typically, an online algorithm receives its input piece by piece, andmust take an irreversible action upon the receipt of each piece of input without knowledge of the future. Suchscenarios are predominant and occur, e.g., in the management of (limited space) cache, in admission and routing incommunication networks, in scheduling, etc. When no prediction of the pattern of the input sequence is available, anaccepted method to analyze the performance of online algorithms is “competitive analysis” [BEY98]. In competitiveanalysis one compares the performance (e.g., overall system cost) of an online algorithm, to the performance of anutopian, clairvoyant, algorithm, that knows the entire input in advance. This type of analysis allows one to obtainrobust results that do not depend on specific input patterns.

Randomization is a very useful tool in the design of online algorithms. Randomized algorithms for such ascenario are many times provably better than deterministic ones. There are many such examples. The most famousone is perhaps the paging problem, where there are randomized paging algorithms which are O(log k) competitive[FKL+91], while there is a lower bound of k on the competitive ratio of deterministic algorithms (k is the numberof pages in the cache) [MMS90]. Other examples are the so-called “call control problem” (see, e.g., [LT94, AAP93,ABFR94, LMSPR01]), or the list-accessing problem (see, e.g., [ST85, RWS94]), to name a few.

Algorithmic Game theory Many distributed systems associate utility functions to quantify some economic value.In recommendations systems [DKR02], customers associate some value with different products, and in classicalGames some utility is assigned to every decision of the players. Classical notions such as Arrow-Debreu equilibriafor recommendation systems and Nash equilibria for games have been introduced in the 1950s. The algorithmicstudy of Nash equilibria started with the work of Lemke and Howson [LH64] in the 1960’s, for the case of twoplayers. This classical algorithm is exponential in the number of strategies (see [SS04b]). Computing a Nashequlibrium is indeed not an easy task. It was proven recently that this computation is complete for the class PPAD,first for r ≥ 4 in [DGP06], then for r ≥ 3 in [DGP05] and [CD05], and finally for r ≥ 2 in [CD06b]. Therefore itis unlikely to be feasible in polynomial time.

Approximate Nash equilibria have been studied both in the additive and the multiplicative models of approxi-mation. An ε-approximate Nash equilibrium describes strategies for each player such that by changing her strategyunilaterally, no player can improve her gain by more than ε. Lipton et al. [LMM03] studied additive approximateNash equilibria for r-player games by considering small-support strategies, and obtained an approximation schemawhich computes an ε-approximate equilibrium in the additive sense, in time nO( ln n

ε2 ), where n is the maximumnumber of pure strategies. It is known that there is no Fully Polynomial Time Approximation Schema for thisproblem [CD06a], but it is open to decide if there is a PTAS. The case of the multiplicative approximation hasbeen studied by Chien and Sinclair [CS07] for dynamic strategies, who also proved a rapid convergence to anapproximate Nash.

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1.2.2 Work package B: QUANTUM COMPUTATION

Quantum Algorithms Quantum computation has been a very active research area for the past decade. Feynmaninitiated the idea of building a computer that exploits laws of quantum mechanics in order to solve computingproblems that could not be solved on current computers. Today, two main results lend credence to this model ofcomputation. P. Shor gave a quantum algorithm that decomposes any integer into its prime factors, in polynomialtime [Sho99], whereas no such algorithm is known in the classical models of computation. This renders vulnerablethe main public key cryptosystems, such as RSA. A few years later, L. Grover gave an algorithm that finds anymarked element in an unstructured list [Gro96], giving a quadratic improvement over the best possble randomizedalgorithm. The main motivation for a quantum computer is to solve tasks more efficiently than classically. Whilethe ultimate goal is an exponential improvement, any polynomial speedup can be helpful as well.

Efficient solutions to some cases of the hidden subgroup problem (HSP), a paradigmatic group theoreticalproblem, constitute probably the most notable success of quantum computing. The problem consists in finding asubgroup H in a finite group G hidden by some function which is constant on each coset of H and is distinct indifferent cosets. The hiding function can be accessed by an oracle, and in the overall complexity of an algorithm,a query counts as a single computational step. To be efficient, an algorithm has to be polylogarithmic in the orderof G. While classically not even query efficient algorithms are known for the HSP, it can be solved efficiently inabelian groups by a quantum algorithm. A detailed description of the so called standard algorithm can be foundfor example in [Mos99]. The main quantum tool of this algorithm is Fourier sampling, based on the efficientlyimplementable Fourier transform in abelian groups. Factorization and discrete logarithm [Sho99] are special casesof this solution.

Discrete time quantum walks were introduced progressively by Meyer[Mey96a, Mey96b] in connection withcellular automata, by Watrous in his works related to space bounded computations [Wat01], and by Ambainis etal [ABN+01]. They can be thought of as the counterpart of classical random walks. Random walks have manyapplications in classical algorithms, and we expect that quantum walks will prove equally important for quantumalgorithms. Furthermore, given the similarities between classical Markov chains and their quantum counterparts,we hope to benefit from the vast existing body of knowledge in the field. Several quantities of quantum walks,like mixing and hitting times, have already been shown to be faster in quantum walks than in the classical case,sometimes even exponentially faster. For example, it has been shown that on an n-dimensional hypercube, reachingthe opposite node by a quantum walk has a polynomial hitting time, whereas a random walk requires exponentialtime [Kem05].

Quantum Lower Bounds and Complexity To understand the advantage of quantum computing over its classicalcounterpart, it is necessary to compare the performance of quantum algorithms to the quantum complexity of theproblem it solves. There has been considerable progress in proving lower bounds in the quantum query model,where one considers how many times an algorithm must consult its input in order to solve the problem. In thismodel, the input is given in the form of an oracle which can be queried by the algorithm, and the complexity is howmany such queries are necessary in order to solve the problem.

Two techniques have been successful in proving quantum lower bounds. The first method is the polynomialmethod, developed in [BBC+01]. In this method, the output probability of a quantum query algorithm is written asa polynomial, whose degree is related to the number of queries made to the oracle. This method has been extendedand applied to prove that the quantum and deterministic query complexities of any total functions are polynomiallyrelated, and also to a variety of problems such as Collision and Element Distinctness problems [AS04].

The second method is known as the adversary method, where the the quantity analysed is by how much inputsmapped to different function values can be distinguished, as the number of queries to the oracle increases. Manyequivalent formulations of this method were formulated [Amb02, BSS03, LM04], and where then shown to beequivalent [SS04a]. These were later shown to imply lower bounds on classical formula size [LLS06].

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Quantum Information and Communication In the process of better understanding quantum and classical in-formation, we would like to investigate their relative power by looking at the model of communication complexity.Communication complexity is related to circuit lower bounds, data structures, automata and many other areas oftheoretical computer science.

The model of communication complexity was first defined by Yao [Yao79], that has found applications in manyareas [KN97]. In this setting, two parties, Alice and Bob, are given some initial inputs and they try to solve a problemthat depends on these inputs. Their goal is to compute the answer using the minimum amount of communication.Alternatively, Alice and Bob try to “encode” the necessary information about their inputs as succinctly as possible.

It is very intriguing to study the relation between classical and quantum communication complexity and henceget a better understanding of classical and quantum information. Examples of problems where quantum commu-nication gives exponential savings were given by Buhrman, Cleve, and Wigderson for one-way and interactiveprotocols with zero error probability [BCW98]; by Raz for bounded-error interactive protocols [Raz99]; and byBuhrman, Cleve, Watrous, and de Wolf for bounded-error simultaneous protocols [BCWW01]. The first two prob-lems are partial Boolean functions, while the third one is a total Boolean function. However, the latter separationdoes not hold in the presence of public coins. Bar-Yossef, Jayram, and Kerenidis [BYJK04] showed an exponentialseparation for one-way protocols and simultaneous protocols with public coins, and this work was followed up byGavinsky, Kempe, Kerenidis, Raz and de Wolf who gave an exponential separation between one-way quantum andclassical communication protocols for a partial Boolean function [GKK+07].

Over the last couple of years the field of quantum information theory has developed increasing connectionsto other areas of theoretical computer science. One such connection that has been discovered recently is betweenquantum computation and classical complexity theory. The goal is to use the rich theory developed for the studyof quantum information as a powerful tool in order to resolve main open questions about classical information andcomputation.

1.2.3 Work package C: INTERACTION BETWEEN CLASSICAL AND QUANTUM COMPUTATION

Research in quantum computation has long benefited from techniques developed for classical computation. Mostof the models of computation, such as query models, communication models, are generalizations of the classi-cal models, and many of the problems studied had been studied previously in classical models. In a surpris-ing new trend, there has been a steady stream of new results in which the contribution flows in the other di-rection, from quantum computation towards classical models, both for algorithms and for lower bounds, includ-ing [SV01, KdW03, Aar04, LM04].

Locally Decodable Codes One of the best known examples of the use of quantum techniques to solve a classicalproblem is the case of locally decodable codes. An error correcting code is locally decodable if any bit of themessage can be decoded by looking at a very few bits of the codeword, even in the presence of errors. Kerenidisand de Wolf [KdW03] have shown the current best lower bound on the number of queries needed to implementclassical locally decodable codes, by applying techniques from quantum information theory.

Classical and Quantum Communication Protocols Physicists have invested a great deal of effort in understand-ing the fundamental problem in quantum information of the nature of correlations exhibited in the measurementsof quantum systems. These were first predicted by Einstein Podolsky and Rosen [EPR35], who viewed these para-doxical correlations as evidence that the quantum model was flawed, or incomplete. Bell [Bel64] formalized thisnotion by showing that no local hidden variable model can reproduce the results of EPR-type experiments, and thecorrelations were observed in laboratory conditions in 1982 [AGR82]. The question of studying how much commu-nication is needed to simulate distributions arising from physical phenomena, such as measuring bipartite quantumstates was posed by Maudlin [Mau92] and the authors who followed [BCT99, CGMP05, DLR05, Ste00, TB03]

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(many of them independently) progressively improved upper bounds on simulating correlations of the 2 qubit sin-glet state. Most recently, Regev and Toner [RT07] proved that two bits of communication suffice to simulate thecorrelations arising from two-outcome measurements of arbitrary-dimension bipartite quantum states. Virtually nonon-trivial upper or lower bounds are known for siumlating more general quantum distributions. This approach tothe communication complexity differs signifcantly from the traditional computer science approach, and we wish tosee what this perspective can bring to the traditional approach.

Circuit Lower Bounds Since proving superpolynomial lower bounds for computational problems of practicalinterest, such as NP-complete problems, turns out to be out of reach of current techniques, much attention has beeninvested in a seemingly easier problem showing superpolynomial lower bounds in the circuit model. In this model,computation is done using circuits composed of AND, OR and NOT gates. Complexity can be measured by thedepth of the best circuit, or by the number of gates in the circuit. Many other variants have been studied as well.Since this is a simpler combinatorial model, it is expected that lower bounds will be easier to prove in this model.Yet even this has turned out to be an extremely difficult problem.

Among the milestones in this line of research are the lower bounds of Khrapchenko [Khr71], and Hastad [Has98],who has shown a lower bound of n3−o(1) for the formula size of an explicit function. Surprisingly, these were shownto be special cases of the quantum adversary method [LLS06]. Karchmer and Wigderson’s characterization of cir-cuit size in terms of communication complexity of relations [KW88] plays an essential role in this connection.In [Ker07] we have also shown a connection between classical circuit depth lower bounds and quantum multipartycommunication complexity.

1.3 Specific aims of the proposal, highlighting the originality and the noveltyOur project’s goal is to perform high caliber original research that stems from theoretical and practical considera-tions in the fields of quantum computing and randomized computing. Our objectives, which will be described indetail in the following section, can be divided in three main categories.

1.3.1 Work package A: RANDOMIZED ALGORITHMS

Property Testing, Streaming Algorithms, Online Algorithms, and Algorithmic Game Theory are important areaswhere to study randomized algorithms. Not only does randomization help in designing better algorithms in theseareas, but furthermore, it is many times possible to prove to what extent randomization improves the performanceof the algorithms, thus allowing to study the power of randomization.

In the present project we would like to study randomized algorithms for a number of problems, with two aimsin mind: (1) improve the state of the art on these specific problems; and (2) advance our knowledge on the powerof randomization in general, and especially in these areas.

Property Testing and Streaming Algorithms First we will pursue the direction of our previous works in PropertyTesting. Then our goal is to move to Streaming Algorithms, and to work specifically on problems for which theProperty Testing approach was studied before. The main motivation is to remove the approximation required byProperty Testing, and adapt the previous testers to Streaming Algorithms. By reading once and sequentially theentire input with polylogarithmic memory space, we hope to remove the approximation inherent to property testing.If this attempt would happen to be unsuccessful, we will keep the same approximation of Property Testing, butwe will try to improve the dependency of the approximation parameter, when that one was intractable for practicalapplications.

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Online Algorithms We plan to further our undestanding of the power of randomization in online computation,by giving novel algorithms for a number of important problems in the area of online algorithms. We are specificallyinterested in, e.g., the following specific problems: (1) improving our previous results on distributed online callcontrol, and giving for the first time also a guarantee on the quality of the selected paths (2) studying streamingalgorithms in distributed settings, and giving for the first time algorithms for this setting that do not rely on routingpaths and (3) improving our previous results on time-constarined scheduling in (linear) networks.

Algorithmic Game theory We intend to investigate how the sampling based techniques for computing approxi-mate additive equilibria of Lipton et al. [LMM03], can be generalized to the multiplicative case. The introductionof the more general McDiarmid’s inequality [McD89], instead of the more classical Hoeffding’s bound results in afiner analysis but the exact limitations of the multiplicative case remain open.

The study of the convergence to approximate Nash equilibria of various dynamics, such as the fictitious player,is a promising area. Some conditions such as the ones presented in [CS07] are often necessary to prove fastconvergence results. In this case, we hope to provide a method for the analysis of approximate mechanisms, i.e.algorithms which guarantee some conditions of an approximate equilibria.


Quantum Algorithms After settling the abelian case, substantial research was devoted to the HSP in some finitenon-abelian groups. Beside being the natural generalization of the abelian case, the interest of this problem is en-hanced by the fact, that important algorithmic problems, such as graph isomorphism, can be cast in this framework.Our approach for addressing this task will be twofold. On the one hand, we will try to extend the the standardalgorithm for the abelian case to non-abelian groups using non-abelian quantum Fourier transforms. This requiresfinding new implementation techniques for this transform, and the determination of classes of group where the ana-logue of the standard abelian algorithm is sufficient for solving the HSP. On the other hand, we also try to exploitsome limited commutativity properties of the given non-abelian group to reduce the problem to simpler instances.

We believe that in order to obtain substantial progress on algorithmic questions, new algorithmic techniqueshave to be developed. To date, there are only a few such techniques, and most efficient quantum algorithms relyon the quantum Fourier transform. An important part of our effort will be dedicated to the research into newalgorithmic techniques, and in particular we intend to explore quantum walks.

Quantum Lower Bounds and Complexity We plan to continue to study quantum lower bounds, in the quantumquery model. Another model we wish to study are time-space tradeoffs. Here, the goal is to see how many morequeries are required if the algorithm can only use a limited amount of quantum memory, and vice versa.

In quantum complexity, we would like to study the role of quantum vs classical advice and proofs. In particular,we would like to study whether the class of problems solved in quantum polynomial time with quantum advice canbe solved with classical advice. Another question we would like to address concerns QMA, the quantum analogueof the class NP. Here, the goal is to prove whether a quantum proof is necessary, or whether a classical proof issufficient.

Quantum Information and Communication Our objective is to study the relation between classical and quan-tum communication complexity and hence gain better understanding of classical and quantum information. Anumber of problems in communication complexity have been already found where quantum protocols need signifi-cantly less communication than classical protocols solving the same problem. We would like to continue this line ofresearch and tackle some of the important open questions regarding quantum communication complexity, includingseparations of classical and quantum communication for total functions and the role of entanglement.

Just as the probabilistic method has become an extremely versatile method of proving purely deterministicstatements in combinatorics by appealing to probabilistic techniques, we would like to explore the possibility of

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a general “quantum method” for applying techniques from quantum information theory to problems in classicalcomplexity theory.


We wish to emphasize this exchange of ideas between quantum and randomized models. We are specialists in bothareas, and we would like to further explore the interactions between randomized and quantum computation. Wedescribe here three examples which illustrate the problems we would like to address.

Locally Decodable Codes We would like to characterise the efficiency of Locally Decodable Codes as a functionof the number of queries and study Locally Checkable Codes and List Decoding. Another problem we wish toconsider is the possibility of a theory of Quantumly Checkable Proofs.

Classical and Quantum Communication Protocols The goal in this workpackage is to bring to communica-tion complexity the insight provided by the physics perspective on simulating quantum and more generally, non-signaling distributions. Another approach involves multiplayer communication complexity [Ker07]. We expect thatstudying the communication complexity of non-signaling distributions will provide a common framework to studythe different models of communication complexity, be they classical, quantum, with and without prior entangle-ment, as well as the simulation of distributions (as opposed to computing functions). This may help understandlower bound methods such as the recent method of Linial and Shraibman.

Non-signaling also suggests a property close to zero-knowledge, and we wish to explore the connections be-tween non-signaling, from the physics perspective, and secure computation.

Circuit Lower Bounds Quantum lower bound techniques, more specifically the adversary lower bounds, havebeen shown to imply lower bounds on purely classical circuit and formula size. These in turn have implications inderandomization. We wish to further see how quantum lower bounds can be used for classical lower bounds, andsee if there are direct connections between these and derandomization.

1.4 Progress beyond the state of the art and relevance to the call for proposalsThe first aim of the project is to maintain the international impact and visibility of our group in randomized andquantum computing topics where we have successfully contributed in the last years in areas such as PropertyTesting, Online algorithms, Quantum Computing, and Complexity. We also want to investigate new and connectedareas such as Streaming Algorithms, Algorithmic Game Theory and Circuit Lower Bounds.

Our group is usually rated as one of the two best teams in Europe in quantum computing (with the group ofHarry Buhrman at CWI in Amsterdam). For randomized computing, we also figure among the best Europeangroups.

Our project fits the two axes of the DEFIS call: “Algorithmes, langages, architectures” (main area) and “Dusignal a l’information, des donnees aux connaissances” (secondary area). Below we describe more specifically howour tasks fit within the sub axes of the call.

• “Algorithmes, langages, architectures” (main area)

– “Algorithmique et preuve”: Property Testing, Streaming Algorithms, Online Algorithms, Quantum Al-gorithms, Locally Decodable Codes

– “Langages et modeles ”: Property Testing (approximation for Model Checking), Algorithmic GameTheory

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– “Nouvelles architectures de composants et de systemes”: Online Algorithms, Quantum Information andCommunication, Classical and Quantum Communication Protocols, Circuit Lower Bounds

• “Du signal a l’information, des donnees aux connaissances”

– “du signal a l’information”: Streaming Algorithms, Online Algorithms (distributed computing part)

– “des donnees aux connaissances”: Property Testing, Streaming Algorithms

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1.5 Detailed description of the work1.5.1 Work package A: RANDOMIZED ALGORITHMS

Property Testing and Streaming Algorithms (Task 1) In the area of numerical computations, we extended theresults of Blum, Luby et Rubinfeld [BLR93] robust to small sublinear and relative errors [KMS03, Mag05]. Wewish to pursue these theoretical results in more applicative areas such as matrix multiplication, FFT, or differentialequations.

With the edit distance, we showed how to ε-test in polylogarithmic time, whether a binary operator given by anN × N matrix defines an abelian group [FIS05], whereas the previous time complexity was O(N3/2) [EKK+00]for the Hamming distance. We want to generalize this approach to other problems on matrices such as properties ofNash equilibria, and important problems in networking.

We also studied words and trees with the edit distance, and generalized the result of [AKNS00], who showedthat regular words are testable for the Hamming distance. We proved [MR07] that regular trees are also testablefor the edit distance with moves, i.e. when subtrees can be moved in one step. In the extension of this workon regular languages, we [FMR06] geometrically characterize words and automata. Context-free languages haveconstant time testers with this distance, whereas there is a Ω(N1/2) lower bound [AKNS00] for the standard Editdistance. Another application is a new notion of approximate equivalence for finite structures, whose decidabilityover context-free languages is possible, whereas the exact version is undecidable. Those results are essentiallyof theoretical interest because of the double exponential dependency on the approximation parameter ε. We alsoobtained only an exponential time algorithm for deciding the equivalence of two regular tree languages, whereasa deterministic and exact algorithm already exists with the same complexity. We conjecture that we could eitherimprove our equivalence tester or make explicit the limitations of our approach.

The area of streaming algorithms has gained increasing attention in recent years [Mut05]. The setting is usuallythat of an algorithm which receives a stream of data items, and has to output some function of the stream, such asthe number of distinct elements, frequency moments, or heavy hitters. The requirement is usually that the spaceused by the algorithm is sublinear in the size of the observed data, and the solution is inherently randomized. Inthe context of verification of XML files according to some given DOM specification, one has to transform first theXML input to a tree. This step is not compatible with Streaming Algorithms since it requires linear memory space.In some specific cases [SV02], there is a possibility to do that verification directly on the XML input. Nonethelessthese cases are too restrictive, namely because of the drastic restriction of constant memory space and deterministicalgorithm.

Classical Model Checking [CGP99] attempts to verify that a given transition system satisfies a property. Thetransition system and the formula are transformed into objects of the same nature, and the algorithmic task is to com-pare them. The objects are typically huge, and their comparison is usually intractable, but we have shown [LLM+06,FMR06] the approximate comparison can be feasible. Property testers introduce new approximation techniques inthis context, which have direct applications for the verification of large structures (Web data, log files), and hugetransitions systems that arise from the execution of a program. The practical applications of these new techniquesrequire their extensions to concurrents systems and to streaming data which have specific constraints. We proposeto extend the approximate verification, based on testers, in three directions. First, to probabilistic and concurrentsystems as presented in PRISM [KNP02]. We intend to generalize the Membership and Equivalence testers in orderto apply these techniques to protocol verification. In this case, we approximate a quantitative property, i.e. decidethat the probability that a property is true is greater than some threshold value. The equivalence testers are polyno-mial in the size of the state space, and can’t be directly used in this context because the state space is too large, butmay admit some useful statistical representation as in evolutionary games. Second, to Black-Box Checking, i.e. todecide if a Black-Box given by its Input-output behaviour satisfies a property. In this case, we learn an approximatemodel, from samples (xi, yi), and check a property of the model as in Model-based testing. Third, to streamingdata, where Testers can be adapted to the Streaming constraints.

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Online Algorithms (Task 2) We have obtained many important results in the area of online algorithms (see,e.g., [LPSR07, RS07, RR05, KR06, AMRR05, LMSPR01]). Recent results include for example refined throughputcompetitiveness results for packet scheduling algorithms [RS07], and randomized distributed algorithms for theonline call control problem [RR05]. We intend to pursue our line of research in order to improve the state of the arton a number of important problems.

The call control problem is defined as follows: A sequence of requests for connections is received in an onlinemanner. Each request consists of a pair of nodes that wish to communicate. For each such request the algorithm hasto immediately either accept the call or reject it. To accept the call the algorithm has to immediately select a virtualcircuit (path) between the communicating parties, obeying the network constraints such as link capacities. The aimof the algorithm is to maximize the number of accepted calls. This problem captures the main algorithmic difficultyin providing Quality-of-Service over packet networks. We would like to have protocols that guarantee a largenumber of serviced requests, on arbitrary network topologies, in the face of arbitrary sequences of requests. Thecurrently known results for this problem on general network topologies give a deterministic online (centralized)algorithm on general networks with an O(log n) competitive ratio [AAP93]. This algorithm requires that eachlink capacity is Ω(log n), where n is the number of nodes in the network. The results in [BFL06] imply that inorder to achieve an o(nε) competitive ratio on general networks by an online (even randomized) algorithm, someminimum edge capacity is required. A distributed randomized protocol for general networks is given in [RR05],and guarantees (with high probability) a polylogarithmic competitive ratio when there is a polylogarithmic lowerbound on the capacity of the edges.

We would like to study a number of open problems along these lines, for example:(1) Devising distributed competitive online protocols for the call control problem that would have linear-size

routing tables at the nodes. The current state-of-the art requires routing tables of quadratic size. Protocols withlinear size routing tables will render these results more compatible with current internet technology.

(2) The current protocols, while guaranteeing high throughput, do not give any guarantee on the “quality” ofthe selected routes. We would like to devise algorithms that in addition to achieving high throughput would alsohave some guarantees on the routes such as maximum dilation, or maximum stretch compared to the shortest pathbetween any two communicating parties.

(3) As a first step in our research, we would like to study the above problems on specific topologies for which itmay be easier to achieve such results. These may be either topologies with specific graph-theoretic properties (e.g.,trees, fixed degree graphs), or topologies that exhibit phenomena that are observed empirically.

In many applications (such as video), packets sent in a communication network must arrive to their destinationby a given deadline, otherwise they are of no use. Previous work on this problem gave online and offline algorithmsthat approximate the optimal solution (and also showed that the problem is NP-hard) [ARSU02, AKRR03, NRS05].However, for the realistic case of networks with buffers, only a logarithmic approximation algorithm is known, evenwhen the network topology is restricted to the line [ARSU02]. We would like to improve these results and to giveonline (or offline) algorithms for the realistic buffered case with constant approximation ratios. Such algorithm willundoubtedly require the use of randomization.

Algorithmic Game theory (Task 3) In [DKR02] we describe an algorithm for competitive recommendationsystems. In this model, we have customers and products and some information about how much a customer likesa specific product. We would like to use this partial information to find which products to recommend to eachcustomer. Our algorithm provides provably good recommendations assuming that every customer rates a smallnumber of the products and that there is a small number of paid customers who test all the products. The algorithmis based on approximate Singular Value Decomposition for the reconstruction of a matrix with few samples. Weprove that for a low-rank matrix, information about a constant number of rows and columns is enough for thereconstruction of the whole matrix with respect to the Frobenius norm. Our work is also a generalization of FastMonte-Carlo Algorithms for finding low-rank approximations by [FKV04]. They describe a way to approximateonly the left (or right, but not both) singular vectors of a matrix. Our approach can approximate both subspaces

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simultaneously. It is remarkable that related techniques have been also successfully applied into the desing ofapproximation algorithms with additive error [FK99]. We plan to continue investigating recommendation systemsthat arise more in practice, for example from sites like amazon.com. There, the information we have is of the formthat some customer prefers product A to product B, instead of how much the customer likes each product. We wantto construct recommendation systems in this model which are provably good and also perform well in practice,using real datasets from sites like amazon.com. For the study of such algorithms we consider higher dimensionalmatrices and compute approximate Singular Value Decompositions of tensors.

In [HRS08] we study approximate Nash equilibria for r-player games, where the number of pure strategies ofthe players is n. We extend the lower bounds on the factors of approximations for strategies with small supportsize. We prove that no ε-approximate equilibrium can be achieved with strategy profiles of support size less thanr−1

√lnn−2 ln lnn−ln r

ln r if ε < r−1r in the additive case, and ε < r − 1 in the multiplicative case. We would like to

know if these lower bounds on the size of the strategy profiles hold also in the case when r = cn, for a constantc ≤ 1. In [HRS08] we also show that for 0 < ε < 1, an ε-approximate Nash equilibrium with support size2r ln(nr+r)

ε2 can be obtained, improving by a factor r the support size of [LMM03]. In an analogous result we showthat for 0 < ε < 1, a multiplicative ε-approximate Nash equilibrium with support size 9r ln(nr+r)

2g2ε2 can be achievedwhere g is a lower bound on the payoffs of the players at some given Nash equilibrium. Can we reduce the gapon the support size between these lower and upper bounds? For example, when r = Θ(1), the lower bound isΩ( r−1

√lnn) and the upper bound is O(lnn). When r = 2, these bounds are tight. Finally let us note, that the main

open problem, both in the two-player and the multi-player case, is the existence of a PTAS.


Quantum Algorithms (Task 4) We have obtained numerous results in this area. In [IMS03], we generalizedand simplified the results of Watrous [Wat01] and Hallgren et al [HRTS03]. In particular, we have solved the HSPin groups with small commutator, and in groups with large center. Our approach has used classical and quantumgroup theoretical tools, but not the non-abelian Fourier transform. In [FIM+03], we have designed an efficientalgorithm for groups of constant exponent and which are solvable with constant derived length. The algorithmproceeds by induction on the length of the composition of the group. The base case of the induction solves theclosely related hidden translation problem in elementary abelian groups. For the inductive step, we define theorbit coset problem, generalizing the above two, and prove that it is auto-reducible to normal subgroups and factorgroups of G. In [FMSS03] we have also improved and extended the work of Buhrman et al [BFNR08] to constructquantum verifiers of properties connected to HSP. Recently, in a series of papers [ISS07, ISS08], we have shownthat the hidden subgroup problem in extraspecial groups and in nil-2 groups, that is in groups of nilpotency classat most 2, can be solved efficiently by a quantum procedure. The quantum part of the algorithm uses well chosengroup actions based on some automorphisms of nil-2 groups. The right choice of the actions requires the solutionof a system of quadratic and linear equations. The existence of a solution is guaranteed by the Chevalley-Warningtheorem, and we prove that it can also be found efficiently.

We wish to pursue this line of research, in particular to give algorithms for more non-abelian cases. Ourreduction presented in [ISS08] for constant class nilpotent groups reduces the HSP to the particular case when thegroup is a p-group of exponent p, and the subgroup is either trivial or cyclic. This reduction suggests as a first stepthe study of nilpotent group of nilpotency class 3. We have some preliminary results suggesting that for certainmatrix groups in this class the problem reduces to solving a system of cubic equations. We hope also to obtain fastalgorithms for further subclasses of nilpotent groups.

The complexity of two special cases of the HSP would be of particular interest. The first one is the hiddensubgroup problem in the symmetric group because it contains as special instance the graph isomorphism prob-lem. The other one is the hidden subgroup problem in the dihedral group because of its relation to certain latticeproblems [Reg04]. For this group, we know that polynomial time quantum Fourier sampling gives out enough

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information to determine the subgroup. Unfortunately, the known classical algorithms for this task require expo-nential time. In a somewhat different approach, Kuperberg has shown that there was a subexponential time quantumalgorithm for this problem. We will try to obtain other subexponential time quantum algorithms, the design of apolynomial algorithm would be a major breakthrough.

Using ideas from hidden subgroup algorithms and in particular, the Fourier transform, we also plan to workon algorithms for other problems in algebraic number theory, such as finding the units of a number field, and theprincipal ideal problem. We would also like to use these techniques to find algorithms for lattice problems.

A particulary promising algorithmic application of quantum walks is searching, and our group has made severalimportant contributions in this direction. We were the first to point out this potential of quantum walks [SKW03]when we designed a quantum walk based simulation of Grover search. Ambainis, in his seminal paper [Amb04],used quantum walks on the Johnson graphs to settle the query complexity of the Element Distinctness problems.Inspired by the work of Ambainis, Szegedy [Sze04] designed a general method to quantize classical Markov chains,and developed a theory of quantum walk based search algorithms. A similar approach for the specific case ofsearching in grids was taken by us in [AKR05]. We successfully applied he frameworks of Ambainis and Szegedyin various contexts to find algorithms with substantial complexity gains over simple Grover search. In particularwe have designed algorithms for finding a triangle in a graph [MSS07], and for deciding if a group operation iscommutative [MN07]. In recent work [MNRS07], we have proposed a new quantum walk based search methodthat expanded the scope of the previous approaches. This algorithm is also conceptually simple, and improvesvarious aspects of many walk based algorithms.

In this context, it is important to continue working on the potential applications of random walks. In partic-ular, we would like to investigate matrix multiplication, and the complexity of deciding if a binary operation isassociative. We would also like to relate quantum walk based search algorithms to the classical hitting time basetechniques. In a different direction, we would like to understand better whether quantum walks can be used to gen-erate certain important quantum states. For instance to solve the Graph Isomorphism Problem it would be sufficientto generate a uniform superposition over all permutations of a graph.

Quantum Lower Bounds and Complexity (Task 5) Quantum complexity gives us a way to determine how wellnew quantum algorithms and protocols fare compared to the theoretical limits on the resources required to carryout the computation. Resources can be time, memory size, communication, randomness, entanglement, numberof qubits, etc. This tells us whether quantum algorithms and protocols can hope to be improved. Another goal ofquantum complexity is to determine whether quantum is inherently better than classical computation, and by whatmargin. Many of the techniques used in classical computing to prove lower bounds on the resources computationaltasks do not carry over easily to quantum models of computation. New techniques, such as the adversary methodand its generalizations [Amb02, LM04, LLS06, HLS07] have been developed. These techniques have been usedto prove optimality results for practical problems such as searching and sorting, shortest paths, and finding localminima in a graph.

Much stronger techniques are needed to prove lower bounds in models that more closely model the operationsof a quantum computational device. Ideally, one would like to prove lower bounds in the quantum circuit model.However, current techniques are such that a general method for proving lower bounds in this model appears to beout of reach in the short term.

We wish to study an intermediate problem, that of proving the analogue of time-space tradeoffs for quantumalgorithms. In the quantum setting, time is replaced with queries to the input, and space is the number of qubitsrequired for the computation. Such time-space tradeoffs have been proven for specific problems such as sort-ing [Kla03] but the methods used so far do not extend to boolean functions.

Another question is that of the power of quantum advice and quantum proofs. We wish to investigate whetherthere is a problem that can be solved efficiently by a quantum computer when given a short quantum advice butcannot be solved efficiently with any classical advice, i.e. whether BQP/poly = BQP/qpoly. Furthermore, wewould like to see if there is a language for which a quantum algorithm can decide membership given a short quantum

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proof, though no classical proof is sufficient, i.e. whether QMA = QCMA.

Quantum Information and Communication (Task 6) Our team has resolved one of the main open questions inquantum communication complexity, i.e. the characterization of the power of quantum one-way communication.In the setting of one-way communication, we only allow a single message from Alice to Bob, or in other words weare looking for an efficient encoding scheme of Alice’s input, such that Bob can retrieve from that the informationthat is necessary to solve the communication problem. In [BYJK04] we proved that quantum encodings can beexponentially more efficient than classical ones. This was the first asymptotic separation in this model. Our resultalso produced the first exponential separation in the model of Simultaneous Messages with public coins. In afollow-up paper [GKK+07] we provided a separation for a more natural type of problems and also showed someinteresting connections between our communication complexity results and the security of quantum key distributionprotocols in the bounded-storage model of cryptography.

The main question that remains unresolved is whether an exponential separation can be achieved for some totalfunction. We would like to investigate this problem building on our previous work on the subject.

One other important question that we would like to investigate is the role of entanglement. Entanglement isat the core of quantum information and its role in the field of quantum communication is vital yet elusive. Morespecifically, we would like to study the role of entanglement in the model of two party communication complexityand investigate whether one can reduce the amount of entanglement that any protocol uses to logarithmic size(compared to the size of the input). Newman’s celebrated result proves that this is true for the amount of sharedrandomness used in communication protocols, however a similar result about entanglement is still not known to betrue or false.


Locally Decodable Codes (Task 7) We have used [KdW03] techniques from quantum computation to answer along standing question about Locally Decodable Codes. An error correcting code is em locally decodable if anybit of the message can be decoded by looking at a very few bits of the codeword (“locally”), even in the presenceof errors. Locally Decodable Codes are central in the study of Probabilistically Checkable Proofs (PCPs), whichare one of the most important results in theoretical computer science of the last decade. Although the statementof the theorem is purely classical, the proof involves quantum techniques in an essential way. This is the firstsuch example and despite attempts by a number of researchers, there has been no success in reconstructing aproof by purely classical arguments. In our result, we reduced a question on the efficiency of Locally DecodableCodes to a related problem in quantum coding theory and used the machinery of Quantum Information Theory,including von Neumann entropy, Holevo’s bound and density matrices, to resolve it. Just as the probabilisticmethod has become an extremely versatile method of proving purely deterministic statements in combinatorics byappealing to probabilistic techniques, we would like to explore the possibility of a general “quantum method” forapplying techniques from quantum information theory to problems in classical complexity theory. In addition, morespecifically, we would like to characterize the efficiency of Locally Decodable Codes as a function of the number ofqueries and study Locally Checkable Codes and List Decoding. In fact some very recent results by Yekhanin showthat certain Locally Decodable Codes can be much more efficient than previously thought.

More specifically, we would like to characterise the efficiency of Locally Decodable Codes as a function of thenumber of queries and study Locally Checkable Codes and List Decoding. Last, we want to address the possibilityof a theory of Quantumly Checkable Proofs.

Classical and Quantum Communication Protocols (Task 8) An important distinguishing feature of quantuminformation is non-locality, as evidenced by the “spooky correlations” of the EPR experiment [EPR35]. Bell [Bel64]formalized this notion by showing that no local hidden variable model can reproduce the results of EPR-typeexperiments.

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We have designed a uniform treatment of the simulation of quantum correlations exhibited by a maximally en-tangled qubit pair [DLR05, DLR07]. In our unifying approach we first reduce this problem to a distributed samplingproblem, and then we show how to solve the latter one by some additional resource, such as communication, post-selection or non-local box. We have also obtained several results on the complexity of simulating more complicatednon-signaling distributions [DKLR08].

Much research in quantum information has been to find novel applications of the non-locality displayed byquantum systems. Quantum teleportation is the best known illustration of this, but there are scores of other exam-ples. To gain a better understanding of quantum non-locality, there is an emerging body of work which goes beyondthe quantum case to a more general setting of non-signaling correlations, that is, where the outcomes of each partydo not convey any information about the experiments carried out by the other party. The correlations achievable byspace-like separated bipartite quantum mechanical systems, indeed of any ’reasonable’ theory of physics, have theproperty of being non-signaling.

The underlying structure of the set non-signaling correlations appears simpler than the quantum case. By study-ing quantum information in this more general setting, we hope to gain a better understanding of the power, and thelimitations, of quantum non-locality. Specifically, we wish to quantify exactly the amount of classical and quantumcommunication, with or without entanglement, required to simulate any non-signaling distribution. Some possibleapplications of this work are

• proving lower bounds in the standard model of classical and quantum communication complexity,

• casting privacy in distributed tasks in terms of non-signaling (where privacy is inherent since no informationis leaked in a non-signaling context),

• applying these results to quantum games such as parity games and unique games, extending to multi-playerscenarios and other related models.

Circuit Lower Bounds (Task 9) One area of investigation that we plan to pursue is in the area of circuit depthlower bounds, a very important but notoriously hard area of classical complexity theory. In [Ker07] we have showna connection between classical circuit depth lower bounds and quantum multiparty communication complexity.Proving a lower bound for the quantum communication complexity model would immediately result in classicalcircuit depth lower bounds, specifically answering a question which has been open for two decades. Recent resultsby Lee in classical and quantum multiparty communication complexity make these connections even stronger. Thisis an extremely interesting avenue of research that we have and continue to pursue. Another way for obtaininglower bounds for the related question of proving formula size lower bounds also arises from quantum techniques,namely the adversary method for lower bounds in quantum query complexity [LM04, SS04a]. Using ideas fromKolmogorov complexity, a notion closely related to information theory, we showed that this method and its manyequivalent formulations can be used to prove strong lower bounds for classical query complexity and formula size,in addition to quantum query complexity. It turns out that the technique generalizes virtually all general techniquesfor formula size, including Hastad’s random restriction technique which he uses to give the best formula size lowerbound to date [LLS06]. We hope that these methods can be extended to improve current best lower bounds forcircuits and formula size, although this is a notoriously difficult problem. We also wish to explore its implications onderandomization, where good circuit lower bounds would lead to effective derandomization. We hope to extend thetechniques to other models such as communication complexity, and hopefully back to the quantum arena where fewgeneral techniques are known to prove lower bounds in this model. Finally, these techniques may be particularlyrelevant for proving lower bounds for sublinear algorithms, where the measure of complexity is the number ofqueries to the input.

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[Kla03] H. Klauck. Quantum time-space tradeoffs for sorting. In Proceedings of the thirty-fifth annual ACM symposium on Theory ofcomputing, pages 69–76, 2003.

[KMS03] M. Kiwi, F. Magniez, and M. Santha. Approximate testing with error relative to input size. Journal of Computer and SystemSciences, 66(2):371–392, 2003.

[KN97] E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997.

[KNP02] M. Kwiatkowska, G. Norman, and D. Parker. Probabilistic symbolic model checking with prism: A hybrid approach. In Proc.TACAS. Springer Verlag, 2002.

[KR06] Alexander Kesselman and Adi Rosen. Scheduling policies for cioq switches. J. Algorithms, 60(1):60–83, 2006.

[KW88] M. Karchmer and A. Wigderson. Monotone connectivity circuits require super-logarithmic depth. In Proceedings of the 20thSTOC, pages 539–550, 1988.

[LH64] C. E. Lemke and J. T. Jr. Homson. Equilibrium points of bimatrix games. Journal of the Society of Industral and AppliedMathematics, pages 413–423, 1964.

[LLM+06] S. Laplante, R. Lassaigne, F. Magniez, S. Peyronnet, and M. de Rougemont. Probabilistic abstraction for model checking: Anapproach based on property testing. ACM Transactions on Computational Logic, 2006. To appear (accepted in 2006).

[LLS06] S. Laplante, T. Lee, and M. Szegedy. The quantum adversary method and formula size lower bounds. Computational Complexity,Special Issue on Complexity, 15(2):163–196, 2006.

[LM04] S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using kolmogorov arguments. InProceedings of the Nineteenth Annual IEEE Conference on Computational Complexity, pages 294–304, 2004.

[LMM03] R. Lipton, E. Markakis, and A. Mehta. Playing large games using simple strategies. In ACM Conference on Electronic Commerce,pages 36–41, 2003.

[LMSPR01] Stefano Leonardi, Alberto Marchetti-Spaccamela, Alessio Presciutti, and Adi Rosen. On-line randomized call control revisited.SIAM J. Comput., 31(1):86–112, 2001.

[LPSR07] Zvi Lotker, Boaz Patt-Shamir, and Adi Rosen. Distributed approximate matching. In PODC, pages 167–174, 2007.

[LT94] Richard J. Lipton and Andrew Tomkins. Online interval scheduling. In SODA, pages 302–311, 1994.

[Mag05] F. Magniez. Multi-linearity self-testing with relative error. Theory of Computing Systems (TOCS), 38(5):573–591, 2005.

[Mau92] T. Maudlin. Bell’s inequality, information transmission, and prism models. In Biennal Meeting of the Philosophy of ScienceAssociation, pages 404–417, 1992.

[McD89] C. McDiarmid. On the method of bounded differences. In Surveys in combinatorics. London Math. Soc. Lectures Notes 141,Cambridge Univ. Press, 1989.

[Mey96a] D. Meyer. From quantum cellular automata to quantum lattice gases. Journal of Statistical Physics, 85(5-6):551–574, 1996.

[Mey96b] D. Meyer. On the abscence of homogeneous scalar unitary cellular automata. Physical Letter A, 223(5):337–340, 1996.

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[MMS90] Mark S. Manasse, Lyle A. McGeoch, and Daniel Dominic Sleator. Competitive algorithms for server problems. J. Algorithms,11(2):208–230, 1990.

[MN07] F. Magniez and A. Nayak. Quantum complexity of testing group commutativity. Algorithmica, 48(3):221–232, 2007.

[MNRS07] F. Magniez, A. Nayak, J. Roland, and M. Santha. Search via quantum walk. In Proceedings of 39th ACM Symposium on Theoryof Computing, pages 575–584, 2007.

[Mos99] Michele Mosca. Quantum Computer Algorithms. PhD thesis, University of Oxford, 1999.

[MR07] F. Magniez and M. de Rougemont. Property testing of regular tree languages. Algorithmica, 49(2):127–146, 2007.

[MSS07] F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. SIAM Journal on Computing, 37(2):413–424, 2007.

[Mut05] S. Muthukrishnan. Data streams: algorithms and applications. Found. Trends Theor. Comput. Sci., 1(2):117–236, 2005.

[NRS05] Joseph Naor, Adi Rosen, and Gabriel Scalosub. Online time-constrained scheduling in linear networks. In INFOCOM, pages855–865, 2005.

[Raz99] R. Raz. Exponential separation of quantum and classical communication complexity. In Proceedings of 31st ACM STOC, pages358–367, 1999.

[Reg04] Oded Regev. Quantum computation and lattice problems. SIAM Journal on Computing, 33(3):738–760, 2004.

[RR05] Harald Racke and Adi Rosen. Distributed online call control on general networks. In SODA, pages 791–800, 2005.

[RS07] Adi Rosen and Gabriel Scalosub. Rate vs. buffer size: greedy information gathering on the line. In SPAA, pages 305–314, 2007.

[RT07] Oded Regev and Ben Toner. Simulating quantum correlations with finite communication. In FOCS ’07: Proceedings of the 48thAnnual IEEE Symposium on Foundations of Computer Science, pages 384–394, Washington, DC, USA, 2007. IEEE ComputerSociety.

[RWS94] Nick Reingold, Jeffery Westbrook, and Daniel Dominic Sleator. Randomized competitive algorithms for the list update problem.Algorithmica, 11(1):15–32, 1994.

[Sho99] Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review,41(2):303–332, 1999.

[SKW03] N. Shenvi, J. Kempe, and K.B. Whaley. Quantum random-walk search algorithm. Physical Review A, 67(052307), 2003.

[SS04a] M. Santha and M. Szegedy. Quantum and classical query complexities of local search are polynomially related. In Proceedings of36th ACM Symposium on Theory of Computing, pages 494–501, 2004.

[SS04b] R. Savani and B. von Stengel. Exponentially many steps for finding a nash equilibrium in a bimatrix game. In IEEE Symposiumon Foundations Of Computer Science, pages 258–267, 2004.

[ST85] Daniel Dominic Sleator and Robert Endre Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202–208, 1985.

[Ste00] Michael Steiner. Towards quantifying non-local information transfer: finite-bit non-locality. Phys. Lett. A, 270:239–244, 2000.quant-ph/9902014.

[SV01] P. Sen and S. Venkatesh. Lower bounds in the quantum cell probe model lower bounds in the quantum cell probe model lowerbounds in the quantum cell probe model. In Proceedings of Intenational Colloquium on Automata, Languages and Programming(ICALP), pages 358–369, 2001.

[SV02] L. Segoufin and V. Vianu. Validating streaming xml documents. In Proceedings of 21st ACM Symposium on Principles of DatabaseSystems, pages 53–64, 2002.

[Sze04] Mario Szegedy. Quantum Speed-Up of Markov Chain Based Algorithms. In Proceedings of the 45th IEEE Symposium onFoundations of Computer Science, pages 32–41, 2004.

[TB03] Ben F. Toner and Dave Bacon. Communication Cost of Simulating Bell Correlations. Phys. Rev. Lett., 91:187904, 2003. quant-ph/0304076.

[Wat01] John Watrous. Quantum algorithms for solvable groups. In STOC ’01: Proceedings of the thirty-third annual ACM symposium onTheory of computing, pages 60–67, New York, NY, USA, 2001. ACM.

[Yao79] A. C-C. Yao. Some complexity questions related to distributive computing. In Proceedings of 11th ACM STOC, pages 209–213,1979.

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1.6 Expected results and potential impactOur project will be successful if the research we perform is considered interesting and important by the scientificcommunity, hence making our group a significant research pole in quantum and randomized computations. Sincethe character of our research is mostly theoretical, the most appropriate way to evaluate our results is by peer review.Our success would be to perform original and novel research that is approved by the researchers in quantum andrandomized computations and hence appear in international conferences and journals.

Moreover, our goal of performing research geared towards implementation and of the dissemination of ourwork can be evaluated based on our scientific collaborations, our participation in national and international scientificmeetings as well as by the number of the invited seminars and lectures our group will give in France and worldwide.

In particular we will organize in 2009 the 24th IEEE Conference on Computational Complexity, the mostprestigious international conference devoted to original research papers in all areas of computational complexitytheory.

Last, we aim at strengthening our group by inviting international researchers for short and mid period and byhiring non-permanent members, including researchers, post doctorate fellows or PhD students.

1.7 Project management: structure and flowThe three workpackages we have defined can be pursued independently throughout the period of the project. Thereare no inter-dependencies that need to be taken into account. There will be progress reports and a final report at theend of the project. Our deliverables throughout the period of the project are publications of original research on thesubjects specified above, national and international collaborations and presentation of our work in scientific venues.

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Permanent membersI. Kerenidis S. Laplante F. Magniez A. Rosen M. de Rougemont M. Santha

TASK 0Coordination R

Work package A: RANDOMIZED ALGORITHMSTASK 1Property Testing andStreaming Algorithms

X R X X X

TASK 2Online Algorithms X R X

TASK 3Algorithmic Game theory X X R X

Work package B: QUANTUM COMPUTATIONTASK 4Quantum Algorithms X R

TASK 5Quantum Lower Boundsand Complexity

X X R X

TASK 6Quantum Informationand Communication

X R

Work package C: INTERACTION BETWEEN CLASSICAL AND QUANTUMTASK 7Locally Decodable Codes R X X

TASK 8Classical and QuantumCommunication Protocols

X R X X

TASK 9Circuit Lower Bounds R X

X: participantR: responsible of the task

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Deliverables and milestonesTask Substance of the deliverables and milestones Delivery dateWork package A: RANDOMIZED ALGORITHMS

1st Report (Publications+Collaborations+Presentations) 122nd Report (Publications+Collaborations+Presentations) 243rd Report (Publications+Collaborations+Presentations) 36Final report for Workpackage A 48

Work package B: QUANTUM COMPUTATION1st Report (Publications+Collaborations+Presentations) 122nd Report (Publications+Collaborations+Presentations) 243rd Report (Publications+Collaborations+Presentations) 36Final report for Workpackage B 48

Work package C: INTERACTION BETWEEN CLASSICAL AND QUANTUM COMPUTATION1st Report (Publications+Collaborations+Presentations) 122nd Report (Publications+Collaborations+Presentations) 243rd Report (Publications+Collaborations+Presentations) 36Final report for Workpackage C 48

1.8 Description of the Consortium1.8.1 Presentation of the relevance of the/each partner to the proposal

Our project brings together experts from both the quantum computation and randomized computation subareas.In quantum computation, we have established ourselves as leaders in algorithms for the hidden subgroup problemand quantum walks (Magniez, Santha), communication complexity (Kerenidis, Laplante), cryptographic protocols(Kerenidis) and the adversary method for proving lower bounds (Magniez, Laplante). In randomized computa-tion, our strengths lie in property testing (Magniez, de Rougement, Santha), approximation algorithms (Kerenidis,Rosen), on-line and distributed algorithms (Rosen), and algorithmic game theory (de Rougemont, Santha). At theintersection of quantum and probabilistic computation, we have estabished ourselves as specialists in locally decod-able codes (Kerenidis), communication protocols and using quantum methods for circuit lower bounds (Kerenidis,Laplante). In both areas, our work involves a large number of international collaborators from top internationalresearch groups.

• Europe

– Germany: Marek Karpinski (University of Bonn)

– Hungary: Gabor Ivanyos, Katalin Friedl (MTA SZTAKI: Computer and Automation Research Instituteof the Hungarian Academy of Sciences)

– Italy: Stefano Leonardi (Universita Roma 1 “La Sapienza”)

– Netherlands: Harry Buhrman, Ronald de Wolf (CWI, Amsterdam)

– Uniter Kingdom: Harald Raecke (Warwick University)

• United States

– Ashish Goel (Stanford)

– T.S. Jayram (IBM)

– Claire Mathieu (Brown University)

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– Ravi Kannan (Yale University)

– Rafail Ostrovsky (UCLA)

– Prabhakar Raghavan (Standford)

– Neil Shenvi, Umesh Vazirani (U.C. Berkeley)

– Mario Szegedy (Rutgers University)

• Canada

– Andris Ambainis, Michele Mosca, Ashwin Nayak (University of Waterloo)

• Israel

– Dorit Aharonov (Hebrew University)

– Ziv Bar-Yossef, Google, Haifa.

– Noga Alon, Julia Kempe, Boaz Patt-Shamir, Oded Regev (Tel Aviv University)

– Eldar Fischer (University of Technion)

– Zvi Lotker (Ben-Gurion University)

– Ran Raz, Weizmann Institute

• Chile

– Marcos Kiwi (Universidad de Chile)

• India

– Pranab Sen, Jaikumar Radhakrishnan (TIFR, Mumbai)

• Singapore

– Artur Ekert (Centre for Quantum Technologies)

• Japan

– Keiji Matsumoto (National Institute of Informatics)

Our group has organized many scientific conferences and events, including:

• 9th Workshop on “Quantum Information Processing”, Carre des Sciences, Paris, 16-20 January 2006. This isthe biggest annual conference in quantum computing, there were about 250 participants.

• EC IST Project QAP workshop, Paris, 12 February 2006.

• EC QIPC Conference, Paris, 13–15 February 2006

• EC IST Project RESQ workshop, Paris, 22-24 March 2006

• Institut Henri Poincare Trimester: Miklos Santha was co-organizer of the IHP trimester on “Quantum Infor-mation, Computation and Complexity”, 4 January–7 April 2006. During the trimester 14 long courses (12hours of lectures) and 10 short courses (6 hours of lectures) were held. The lectures were filmed and areaccessible at http://cel.ccsd.cnrs.fr. The number of participants was 120.

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• Adi Rosen was co-organizer of the Bertinoro Workshop on Adversarial Modeling and Analysis of Commu-nication Networks (November 2006).

Our group has been recently involved in the following projects:

• Project ANR Blanc “AlgoQP” (Algorithmique et complexite quantique et probabiliste), 2005-08. PI SophieLaplante, amount awarded 280K euros.

• Project ANR Sesur “VERAP” (Approximate Verification of Probabilistic Systems), 2007-10. PI Michel deRougemont, amount awarded 160K euros.

• EC 6th framework integrated project IST-2003-015848 “QAP” (Qubit Applications), 2005-09. PI for LRIMiklos Santha, amount awarded 160K euros.

For completeness, short CVs of permanent members are listed in Appendix 2.1.6, excepted the one of theprincipal investigator which is included in Section 1.8.3.

1.8.2 Description of complementarities within the consortium (if several partners)

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1.8.3 Principal investigator: skills and CV

Frederic Magniez, Charge de Recherche CNRS, LRI

Personnal informations• Born: 2 mai 1971

• Address: LRI, batiment 490, Universite Paris-Sud, 91405 ORSAY Cedex

• Tel.: +33 1 69 15 42 48, fax: +33 1 69 15 65 86

• E-mail: [email protected]

• Web page: http://www.lri.fr/˜magniez

Education• 2000: Ph.D. in Computer Science with Miklos Santha at LRI, Universite Paris-Sud, France

Subject: Self-testing in approximate and quantum computations

• 1995: M.S. in Computer Science and Agregation of Mathematiques at Ecole Normale Superieure, Cachan,France

Honors and Awards• 2000: Ph.D. award by Association Francaise d’Informatique Theorique

• 1995: Ranked 60th in France at the Agregation de Mathematiques

Professional Experience• 2003-...: Assistant professor at Ecole Polytechnique, France

• 2000-...: CNRS researcher at LRI

ResearchInterests

Quantum Computing (algorithms and cryptography), Property Testing, Streaming Algorithms, Approximation inVerification

Administration

• Leader of the CNRS working group “Quantum Computing” since 2006, part of GDR “Informatique Mathematique”

• Co-leader with Ashwin Nayak, IQC, University of Waterloo, of the grant “Quantum algorithms and complex-ity theory” from the France-Canada Research Foundation, 10 KCAD , 2007-08

• Leader of the grant “Quantum Cryptanalysis” from the French Research Ministry, 75 KEUR, 2002-05

• Recently participant of the following grants:

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– “Quantum and Randomized Algorithms and Complexity” from the French Research Ministry, 280KEUR, 2005-08, leader: Sophie Laplante, LRI

– “Qubit Applications”, EU 6th framework, 165 KEUR, 2005-08, leader: Miklos Santha, LRI– “Approximate Verification of Probabilistic Systems” from the French Research Ministry, 162 KEUR,

2007–10, leader: Michel de Rougemont, LRI

• Member of the CNRS research group Quantum Information and Communication, leader: Jean-PhilippePoizat, UJF Grenoble

• Member of the hiring committee of the CS Dept of University Paris-Sud since 2004

• Member of the teaching committee of the CS Dept of the Ecole Polytechnique of France

Evaluation

• Referee for the 2007 ERC Starting Grants - 2nd Stage

• Referee for a grant application to the Israel Science Foundation

• Referee for a local french grant application

• Referee for journal articles: SIAM Journal on Computing, Theory of Computing, Theoretical Computer Sci-ence, Journal of Discrete Algorithms, Quantum Information and Computation, journal Foundations of Com-putational Mathematics, Encyclopedia of Algorithms

• Referee for conference articles: IEEE Symposium on Foundations of Computer Science, ACM Symposiumon the Theory of Computing, IEEE Symposium on Logic in Computer Science, IEEE Computational Com-plexity Conference, Symposium on Principles of Database Systems, International Colloquium on AutomataLanguages and Programming, Symposium on Theoretical Aspects of Computer Science, ACM Symposium onParallelism in Algorithms and Architectures, Computer Science and Logic, Latin American Theoretical In-formatics, Foundations of Software Technology and Theoretical Computer Science, International Conferenceon Cryptology in India, ERATO Conference on Quantum Information Science

Committees

• Co-editor with Ashwin Nayak of the Quantum Computation special issue of Algorithmica

• Program committees:

– 25th Symposium on Theoretical Aspects of Computer Science, Bordeaux 2008– 16th International Symposium on Fundamentals of Computation Theory, Budapest 2007– 9th Workshop on Quantum Information Processing, Paris 2006– 31st Annual Conference on Current Trends in Theory and Practice of Informatics, Slovak Republic

2005

• Organizing committees:

– 9th Workshop on Quantum Information Processing, Paris 2006– Ecole de printemps d’informatique theorique, Montignac 2005– Workshop AS STIC Nouveaux modeles de calculs : Algorithmes et complexite, Paris 2002

• Vulgarization : Co-author of an article for the french journal La Recherche, “Comment calculer quantique”,398:30-37, juin 2006

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Teaching2006-: Responsible and lecturer of the course “Randomized Algorithms and Complexity” for the CS Master program

of University Paris 7

2003-: Lecturer at the Ecole Polytechnique of France in programming, algorithms, and quantum computing

2005-: Member of the entrance examination committee for CS at the Ecole Polytechnique of France

2003-05: Member of the entrance examination committee for CS at the Ecole Centrale-Supelec

2002-06: Lecturer in CS Master program of Universite Paris 7

2000-02: T.A. lecturer in CS Licence program at University Paris-Sud

StudentsPhD

2007-: Loıck Magnin, “Quantum information with continuous variables”, co-advising with Nicolas Cerf, QuIC,Universite Libre de Bruxelles,

2000-03: Sylvain Peyronnet, “Model checking and probabilistic verification”, partly involved in the advising withMichel de Rougemont, LRI

Master

2007: (M2 MIF ENS-Lyon), L. Magnin, “Quantum protocols with continuous variables”

2006: (M2 MPRI), B. Couetoux, “Lower bounds of boolean functions”

2003: (DEA DIF ENS-Lyon), P. Philipps, “Quantum lower bounds: adversary method vs polynomial method”

2002: (DEA Algo), K.-F. Lin, “Quantum computing by adiabatic evolution”

PhD committee

2005: Member of the PhD committee of Emmanuel Jeandel, “Algebraic techniques in quantum computing”, ENS-Lyon

Publications

Refereed journal articles1. H. Buhrman, C. Durr, M. Heiligman, P. Høyer, F. Magniez, M. Santha, and R. de Wolf. Quantum algorithms

for element distinctness. SIAM Journal on Computing, 34(6):1324–1330, 2005.

2. W. van Dam, F. Magniez, M. Mosca, and M. Santha. Self-testing of universal and fault-tolerant sets ofquantum gates. SIAM Journal on Computing, 37(2):611–629, 2007.

3. G. Ivanyos, F. Magniez, and M. Santha. Efficient quantum algorithms for some instances of the non-abelianhidden subgroup problem. International Journal of Foundations of Computer Science, 14(5):723–740, 2003.

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4. M. Kiwi, F. Magniez, and M. Santha. Approximate testing with error relative to input size. Journal ofComputer and System Sciences, 66(2):371–392, 2003.

5. S. Laplante, R. Lassaigne, F. Magniez, S. Peyronnet, and M. de Rougemont. Probabilistic abstraction formodel checking: An approach based on property testing. ACM Transactions on Computational Logic, 2006.To appear.

6. S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using Kolmogorovarguments. SIAM Journal on Computing, 2006. To appear.

7. F. Magniez. Multi-linearity self-testing with relative error. Theory of Computing Systems (TOCS), 38(5):573–591, 2005.

8. F. Magniez and A. Nayak. Quantum complexity of testing group commutativity. Algorithmica, 48(3):221–232, 2007.

9. F. Magniez and M. de Rougemont. Property testing of regular tree languages. Algorithmica, 49(2):127–146,2007.

10. F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. SIAM Journal onComputing, 37(2):413–424, 2007.

Refereed conference articles1. H. Buhrman, C. Durr, M. Heiligman, P. Høyer, F. Magniez, M. Santha, and R. de Wolf. Quantum algorithms

for element distinctness. In Proceedings of 15th IEEE Conference on Computational Complexity, pages131–137, 2001.

2. W. van Dam, F. Magniez, M. Mosca, and M. Santha. Self-testing of universal and fault-tolerant sets ofquantum gates. In Proceedings of 32nd ACM Symposium on Theory of Computing, pages 688–696, 2000.

3. K. Friedl, G. Ivanyos, F. Magniez, M. Santha, and P. Sen. Hidden translation and orbit coset in quantumcomputing. In Proceedings of 35th ACM Symposium on Theory of Computing, pages 1–9, 2003.

4. E. Fischer, F. Magniez, and M. de Rougemont. Approximate satisfiability and equivalence. In Proceedingsof 21st IEEE Symposium on Logic in Computer Science, pages 421–430, 2006.

5. K. Friedl, F. Magniez, M. Santha, and P. Sen. Quantum testers for hidden group properties. In Proceedingsof the 28th International Symposium on Mathematical Foundations of Computer Science, volume 2747 ofLecture Notes in Computer Science, pages 419–428. Springer, 2003.

6. G. Ivanyos, F. Magniez, and M. Santha. Efficient quantum algorithms for some instances of the non-abelianhidden subgroup problem. In Proceedings of 13th ACM Symposium on Parallelism in Algorithms and Archi-tectures, pages 263–270, 2001.

7. M. Kiwi, F. Magniez, and M. Santha. Approximate testing with relative error. In Proceedings of 31st ACMSymposium on Theory of Computing, pages 51–60, 1999.

8. S. Laplante, R. Lassaigne, F. Magniez, S. Peyronnet, and M. de Rougemont. Probabilistic abstraction formodel checking: An approach based on property testing. In Proceedings of 17th IEEE Symposium on Logicin Computer Science, pages 30–39, 2002.

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9. S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using Kolmogorovarguments. In Proceedings of 19th IEEE Conference on Computational Complexity, pages 214–304, 2004.

10. F. Magniez. Multi-linearity self-testing with relative error. In Proceedings of 17th Symposium on TheoreticalAspects of Computer Science, volume 1770 of Lecture Notes in Computer Science, pages 302–313. Verlag,2000.

11. F. Magniez, D. Mayer, M. Mosca, and H. Ollivier. Self-testing of quantum circuits. In Proceedings of33rd International Colloquium on Automata, Languages and Programming, volume 4051 of Lecture Notesin Computer Science, pages 72–83. Verlag, 2006.

12. F. Magniez and A. Nayak. Quantum complexity of testing group commutativity. In Proceedings of 32ndInternational Colloquium on Automata, Languages and Programming, volume 1770 of Lecture Notes inComputer Science, pages 1312–1324. Verlag, 2005.

13. F. Magniez, A. Nayak, J. Roland, and M. Santha. Search via quantum walk. In Proceedings of 39th ACMSymposium on Theory of Computing, 2007.

14. F. Magniez and M. de Rougemont. Property testing of regular tree languages. In Proceedings of 31stInternational Colloquium on Automata, Languages and Programming, volume 3142 of Lecture Notes inComputer Science, pages 932–944. Verlag, 2004.

15. F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. In Proceedings of16th ACM-SIAM Symposium on Discrete Algorithms, pages 1109–1117, 2005.

Others1. J. Kempe, S. Laplante, and F. Magniez. Comment calculer quantique. La Recherche, 398:30–37, June 2006.

2. M. Kiwi, F. Magniez, and M. Santha. Exact and approximate testing/correcting of algebraic functions: Asurvey. In Proceedings of 1st Summer School on Theoretical Aspects of Computer Science, volume 2292 ofLecture Notes in Computer Science, pages 30–83. Verlag, 2000. Also ECCC Report TR01-014.

3. F. Magniez. Auto-test pour les calculs approche et quantique. PhD thesis, Universite Paris-Sud, France,2000. Record number 6076.

4. F. Magniez. Verification approchee - Calcul quantique. Habilitation, Universite Paris-Sud, France, 2007.Record number 1018.

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1.9 Data management, data sharing, intellectual property strategy, and exploitation ofproject results

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2 Requested budget: detailed financial plan

2.1 Partner 1The following budget is computed on the basis of a 4-year project. Due to the multiple overlaps of the participantsin the different tasks, it would not be meaningful to distribute the budget among the specific tasks. Each task havingapproximately the same scope and requiring similar human and budgetary resources, we expect to distribute theglobal budget among them in equal parts. For the sake of clarity we list the budget under Task 0 in document A.

2.1.1 Large equipment

There is no large equipment needed for the project.

2.1.2 Personnel

• Permanent members:

1. Iordanis Kerenidis, 70 %, Charge de Recherche CNRS, LRI, 53,408.97 euros/year

2. Sophie Laplante, 70 %, Professor University Paris-Sud, LRI, 33,469.71 euros/year (*)

3. Frederic Magniez, 70 %, Charge de Recherche CNRS, LRI, 63,889.21 euros/year

4. Adi Rosen, 70 %, Directeur de Recherche CNRS, LRI, 66,273.89 euros/year

5. Michel de Rougemont, 50 %, Professor University Paris II, LRI, 50,539.15 euros/year(*)

6. Miklos Santha, 70 %, Directeur de Recherche CNRS, LRI, 91,099.97 euros/year

(*): For faculty members, this represents the real salary divided by 2The number of permanent members in the project is 192 people·months, for a cost of 963,875.20 euros.

• PhD students (3,000 euros/month per student):

1. Andre Chailloux, 3 years, 40 %, advisor: Iordanis Kerenidis

2. Sebastien Hemon, 1 year, 80 %, advisor: Miklos Santha

3. Marc Kaplan, 1 year, 80 %, advisor: Sophie Laplante

4. Loıck Magnin, 3 years, 40 %, advisor: Frederic Magniez

5. Mathieu Tracol, 3 years, 40 %, advisor: Michel de Rougemont

The number of PhD students in the project is 62.4 people·months, for a cost of 187,200 euros.

• Project financed non-permanent members

1. Postdocs: 2 years, 100 %, 4,000 euros/month

2. PhD student: 3 years, 100 %, 3,000 euros/month

3. Internship students: 40 months (2 students per year), 100 %, 400 euros/month

The number of project financed non-permanent members is 100 people·months, for a cost of 220,000 euros.

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We would like to hire postdoctoral fellows for a total duration of twenty-four months. There is a possibility ofhiring one fellow for two years or more fellows for shorter durations. In the case suitable candidates are not found,we would like to attribute the positions to visiting junior researchers with a PhD degree. They will be members ofthe project for 100% of their research time.

Candidate profile: Previous research in the field of quantum or randomized computation. Due to the interdis-ciplinary character of the project, the candidates may have diverse backgrounds, including in computer science,mathematics, information theory or physics. The topic of the research will be decided according to the needs of theproject at that time.

Our PhD students usually get financial support from the French Ministry of Research through University Paris-Sud, Ecole Normale Superieure (Paris, Cachan and Lyon), or Ecole Polytechnique. However, we would like to hireone PhD student specifically on the project on our budget.

2.1.3 Services, outward facilities

We will not use any external services.

2.1.4 Travel

One of the crucial factors towards the success of our project is our ability to collaborate with researchers at thenational and international level and participate in scientific meetings and conferences in order to disseminate ourwork. Our team members have a very strong record of collaborations that has led to original and novel researchpublished in the most important venues in the field.

The budget of 200K euros guarantees the continuation and expansion of our productive interaction with thenational and international scientific community. It will support the travel costs of our team members to otherresearch units and also the visits of acclaimed researchers to our laboratory.

For example, a 2-week visit to and from North America costs around 2K euros. The project group has anaverage of 10 people per year. Therefore 200K euros corresponds to 2.5 such visits per year and per member.

2.1.5 Expenses for inward billing

We will not have any expenses for inward billing.

2.1.6 Other expenses

The other expenses of 80K euros for the entire duration of the project consist of consumables, small equipment(less than 4,000 each) such as desktop and laptop computers, and computing equipment, office material, and variousexpenses conducive to the success of the project.

We plan to buy a laptop (2K euros) and a desktop (2K euros) for every participant of the group, namely ap-proximately 15 people. This amounts to 60K euros. The rest of 20K euros will be spent in the other mentionedcategories.

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Annexes

Iordanis Kerenidis, Charge de Recherche CNRS, LRI

Employment• 2006 – now: CNRS - Universite de Paris-Sud XI

Chercheur CNRS (CR2) at the Laboratoire de Recherche en Informatique

• 2004 – 2006: Massachusetts Institute of TechnologyPostdoctoral Associate in the Dept. of MathematicsSupervisor: Peter Shor

Education• 2000 – 2004: University of California, Berkeley

Ph.D. in Computer ScienceThesis: Quantum Encodings and Applications to Locally Decodable Codes and Communication ComplexityAdviser: Umesh Vazirani

• 1995 – 2000: National Technical University of TechnologyGRAD. in Electrical and Computer EngineeringUndergraduate Thesis: A survey on Quantum ComputationAdviser: Eustathios Zachos, GPA: 9.5/10.0 (1st in the University)

Visiting Researcher• Princeton University, Fall 2007. Massachusetts Institute of Technology, Fall 2007, Spring 2006. Californian

Institute of Technology, Fall 2006. Institute of Pure and Applied Mathematics (IPAM), Fall 2006. Universityof California, Berkeley, Fall 2006, Spring 2005. Institut Henri Poincare, Winter 2006. University of Waterloo,Summer 2005. Laboratoire de Recherche en Informatique, Spring 2005

Awards/Grants• Responsible of Strategic French-Japanese Cooperative Program on Information and Communications Tech-

nology (ICT) “Quantum Computation: Theory and Feasibility”, 2008-2010.

• Recipient of Marie Curie International Reintegration Grant, 2006-2008.

• Member of ANR (Agence Nationale de la Recherche, France) “Algorithmique et Complexite Quantique etProbabiliste” (2005-2008).

• Member of QAP, 6th European Framework (Nov. 2005 - Oct. 2009).

• Member of the Steering Committee of “GdR Information et Communication Quantique” (2005-2008).

• Member of “Theory of Algorithms and Logic: Applications to Computer Science”, Pythagoras grant of theOperational Programme on Education and Initial Vocational Training, (2004–2006).

• UC Berkeley Regents Fellowship, 2000-2003

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• Award for highest GPA among all graduating students at NTU, Athens.

• Scholarships from the Greek Fellowship Foundation for highest academic achievement, 1995-1999

• Member of the Greek National Team at the ACM Programming Contest, 1999

• 9 awards in Greek National Math, Physics and Chemistry Competitions, 1990-1994

Teaching/Advising• “Quantum Information and Applications” 2007-2008 at the Master Parisien de Recherche en Informatique.

• “Quantum Information and Applications” 2006-2007 at the Master Parisien de Recherche en Informatique.

• “Number Theory and Cryptography”, National Technical Univ. Athens, 1999.

Students: Andre Chailloux (PhD), Anna Pappa (Master)

Research interestsQuantum Computation, Complexity Theory, Quantum Cryptography, Web Algorithms

Selected Publications• Interactive and Noninteractive Zero Knowledge are Equivalent in the Help Model

Andre Chailloux, Dragos Florin Ciocan, Iordanis Kerenidis, Salil VadhanTheory of Cryptography Conference (TCC) 2008.

• Exponential separations for one-way quantum communication complexity, with applications to cryp-tographyDmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, Ronald de WolfProceedings of ACM STOC 2007.

• Quantum Multiparty communication complexity and circuit lower bounds,Iordanis Kerenidis4th Annual Conference on Theory and Applications of Models of Computation,Journal version: Special Issue for TAMC 2007 in “Mathematical Structures in Computer Science”, to appear

• Exponential separation of quantum and classical one-way communication complexityZiv Bar-Yossef, T. S. Jayram, Iordanis KerenidisProceedings of ACM STOC 2004, p. 128-137.Journal version: SIAM Journal of Computing, to appear

• Exponential Lower Bound for 2-Query Locally Decodable Codes via a quantum argumentIordanis Kerenidis, Ronald de WolfProceedings of ACM STOC 2003, p. 106-115, 2003Journal version: Special issue for STOC 2003 at Journal of Computer and System Sciences (JCSS), 69(3):395-420, 2004

• Competitive Recommendation SystemsP. Drineas, I. Kerenidis, P. RaghavanProceedings of ACM STOC 2002, p. 82-90.

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Sophie Laplante, Professeur Universite Paris-Sud XI, LRI

EducationUniversite Paris-Sud, Orsay 2005Habilitation a diriger des recherchesThesis title: Applications de la complexite de Kolmogorov a la complexite classique et quantique

University of Chicago, Paris 1991 - 97Ph.D. Computer ScienceAdvisor: Lance FortnowThesis title: Kolmogorov Techniques in Computational Complexity Theory

EmploymentUniversite Paris-Sud XI 2006 - presentProfessor in Computer Science

Universite Paris-Sud, IUT d’Orsay 2000 - 06Maıtre de conferences (Assistant Professor) in CS

Universite Paris-Sud, LRI 1997 - 2000ATER and Postdoctoral researcher

Research interestsQuantum computing, probabilistic algorithms, computational complexity

Ph.D. StudentsPh.D. Advisor in CS at the Universite Paris-Sud of 2 students between 2006 and 2008

Steering Committees1. Journees francaises sur la Theorie Algorithmique de l’Information. (2000–2003.)

Program Committees1. IEEE Conference on Computational Complexity 2002.

2. STACS 2006

3. Computability in Europe 2008

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Selection of publications1. L. Fortnow and S. Laplante. Circuit lower bounds a la Kolmogorov. Information and Computation, 123(1),

1995.

2. A. Berthiaume, W. van Dam, and S. Laplante. Quantum Kolmogorov complexity. JCSS, Special Issue onComplexity 2000., 63(2):201–221, 2001.

3. S. Laplante, T. Lee, and M. Szegedy. The quantum adversary method and classical formula size lowerbounds. Computational Complexity, Special Issue on Complexity 2005, 15 (2) 2006, 163-196

4. J. Degorre, S. Laplante, J. Roland. Simulation of bipartite qudit correlations In PRA, Vol.75, No.1, 2007.

5. S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using kolmogorovarguments. SIAM Journal on Computing, to appear.

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Adi Rosen, Directeur de Recherche CNRS, LRI

Academic DegreesPh.D. in Computer Science, Tel-Aviv University, 1995. Advisor: Prof. Amos Fiat.

M.Sc. in Computer Science, Tel-Aviv University, 1990 (Cum Laude). Advisor: Prof. Yehuda Afek.

B.Sc. in Mathematics and Computer Science, Tel-Aviv University, 1987 (Cum Laude).

Academic Appointments2005 – – Directeur de Recherche CNRS DR2, at Laboratoire de Recherche en Informatique (LRI), University of

Paris 11, Orsay.

2000–2005 – Senior Lecturer, Department of Computer Science, Technion - Israel Institute of Technology, Israel.

1999 – Research Associate, Department of Computer Science, University of Toronto.

1995–1998 – Postdoctoral Fellow, Department of Computer Science, University of Toronto.

1991–1995 – Instructor, Department of Computer Science, Tel-Aviv University.

Research InterestsAlgorithms and protocols in communication networks, Online algorithms, Private computation

Public Professional ActivitiesProgram committee member: STACS 2009; PODC 2008; APPROX 2008; SCN 2008; WAOA 2007; WEA 2006;

IPDPS 2006; SPAA 2005; ICALP 2005; ESA 2005; WAOA 2005

co-Organizer of Bertinoro Workshop on Adversarial Modeling and Analysis of Communication Networks (Novem-ber 2006)

Publications in the last 5 yearsRefereed Papers in Professional Journals

[1] M. Adler, S. Khanna, R. Rajaraman, A. Rosen, Time-Constrained Scheduling of Weighted Packets on Treesand Meshes. Algorithmica, Vol. 36, No. 2, pp. 123–152, 2003.

[2] E. Kushilevitz, R. Ostrovsky, A. Rosen, Amortized Randomness in Private Computations. SIAM journal onDiscrete Mathematics, Vol. 16, No. 4, pp. 533–544, 2003.

[3] Z. Lotker, B. Patt-Shamir, A. Rosen, New Stability Results for Adversarial Queuing. SIAM journal on Com-puting, Vol. 33, No. 2, pp. 286–303, 2004.

[4] M. Adler, A. Rosen, Tight Bounds for the Performance of Longest in System on DAGs. Journal of Algo-rithms, Vol. 55, No. 2, pp. 101–112, 2005.

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[5] W. Aiello, Y. Mansour, S. Rajagopolan, A. Rosen, Competitive Queue Policies for Differentiated Services.Journal of Algorithms, Vol. 55, No. 2, pp. 113–141, 2005.

[6] A. Gal, A. Rosen, Ω(log n) Lower Bounds on the Amount of Randomness in 2-Private Computation. SIAMjournal on Computing, Vol. 34, No. 4, pp. 946–959, 2005.

[7] A. Kesselman, A. Rosen, Scheduling Policies for CIOQ Switches. Journal of Algorithms, Vol. 60, No. 1, pp.60–83, 2006.

[8] A. Kesselman, A. Rosen, Controlling CIOQ Switches with Priority Queuing and in Multistage Interconnec-tion Networks. Accepted for publication in Journal of Interconnection Networks.

[9] A. Rosen, M. S. Tsirkin, On Delivery Times in Packet Networks under Adversarial Traffic. Theory of Com-puting Systems, invited paper to the Special Issue for SPAA 2004, Vol. 39, No. 6, pp. 805–827, 2006.

ConferencesRefereed Papers in Conference Proceedings

[10] W. Aiello, E. Kushilevitz, R. Ostrovsky, A. Rosen, Dynamic Routing on Networks with Fixed-Size Buffers,In Proc. of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 771–780, January2003.

[11] A. Gal, A. Rosen, Lower Bounds on the Amount of Randomness in Private Computation, In Proc. of the 35thAnn. ACM Symposium on the Theory of Computing (STOC), pp. 659–666, June 2003. (early version of [6]).

[12] A. Kesselman, A. Rosen, Scheduling Policies for CIOQ Switches, In Proc. of the 15th ACM Symposium onParallel Algorithms and Architecture (SPAA), pp. 353–362, June 2003. (early version of [7]).

[13] D. Guez, A. Kesselman, A. Rosen, Packet-Mode Policies for Input-Queued Switches, In Proc. of the 16thACM Symposium on Parallel Algorithms and Architecture (SPAA), pp. 93–102, June 2004.

[14] A. Rosen, M. S. Tsirkin, On Delivery Times in Packet Networks under Adversarial Traffic, In Proc. of the16th ACM Symposium on Parallel Algorithms and Architecture (SPAA), pp. 1–10, June 2004. Invited paperto the Special Issue for SPAA 2004 (Theory of Computing Systems). (early version of [9]).

[15] H. Racke, A. Rosen, Distributed Online Call Control on General Networks, In Proc. of the 16th AnnualACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 791–800, January 2005.

[16] J. Naor, A. Rosen, G. Scalosub, Online Time-Constrained Scheduling in Linear Networks. In Proc. of IEEEINFOCOM 2005, March 2005.

[17] E. Gordon, A. Rosen, Competitive Weighted Throughput Analysis of Greedy Protocols on DAGs. In Proc.of the 24th Ann. ACM Symposium on Principles of Distributed Computing (PODC), pp. 227–236, July 2005.

[18] A. Rosen, G. Scalosub, Rate vs. Buffer Size - Greedy Information Gathering on the Line. In Proc. of the19th ACM Symposium on Parallel Algorithms and Architecture (SPAA), pp. 305–314, June 2007.

[19] Z. Lotker, B. Patt-Shamir, A. Rosen, Distributed Approximate Matching. In Proc. of the 26th Ann. ACMSymposium on Principles of Distributed Computing (PODC), pp. 167–174, August 2007.

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Michel de Rougemont, Professeur Universite Paris II, LRI

Education• 1988: Habilitation a diriger des recherches, University Paris-Sud, Orsay, France.

• 1983: Ph.D., University of California at Los-Angeles, USA.

• 1976: Master of Sciences in Computer Science, University of California at Berkeley, USA.

• 1975: Ingenieur des Telecommunications, Ecole Nationale Superieure des Telecommunications, Paris.

Positions• Since 1995, Professor of Computer Science, University Paris-II,

• 1995 (March, April, May): Visiting Professor at ICSI (International Computer Science Institute), Universityof California at Berkeley, (On leave from University Paris-Sud and ENSTA),

• 1988-1995, Researcher at Laboratoire de Recherche en Informatique, CNRS and University Paris-Sud. Pro-fessor at Ecole Nationale Superieure de Techniques Avancees (ENSTA), Paris,

• 1987-1988, Associate Professor, University Paris-South,

• 1984-87, Researcher at E.C.R.C. (European Computer-Industry Research Centre, Munich, Germany ),

• 1979, INRIA Scholar (at UCLA).

• 1977-78, Assistant at the Universitad Autonoma de Mexico.

Research Interests• Logic and complexity, Applications to Databases and Problems with Uncertainty.

• Member of program commitees of conferences such as, IEEE Symposium on Logic in Computer Science(LICS), ACM Principles of Database Systems (PODS), International Conference on Electronic Business.

• Adviser of 11 Thesis Ph.D. students since 1990, 2 current Ph.D. students.

Publications6 Books, 16 articles in journals (13 international, 3 national), 41 articles in conferences (37 international, 4 national).

Publications since 2004• Logic and Complexity, Book with Springer-Verlag, 2004.

• Property testing on tree regular languages, ICALP 2004, (with Frederic Magniez).

• Correctors for XML data, XSym 2004, (with Utsav Boobna).

• Approximate schemas and Query Answering, ISIP’05 (Second Franco-Japanese Workshop on InformationSearch, Integration and Personalization), Lyon 2005.

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• Approximate Satisfiability and Equivalence, (with E. Fischer and F. Magniez) IEEE Symposium on Logic inComputer Science, (LICS), 2006.

• A Model of Uncertainty for Near-Duplicates in Document Reference Networks(with C. Hess). ECDL 2007:449-453

• Property Testing for Approximate Search and Integration, ISIP’07 (Third Franco-Japanese Workshop onInformation Search, Integration and Personalization), Sapporo 2007.

• Probabilistic Abstraction in Model Checking (avec S. Laplante, R. Lassaigne, F. Magniez et S. Peyronnet),ACM Transactions on Computational Logic, 2007.

• Uniform generation in spatial constraint databases and applications (with D. Gross) . J. Comput. Syst. Sci.72(4): 576-591 (2007)

• Property testing on tree regular languages, (with Frederic Magniez), Algorithmica, 2007 (49), pages 127-146.

• Approximate Data Exchange (with A. Vielleribiere), International Conference on Database Theory, ICDT,2007.

• Approximate Nash Equilibria for Multi-player Games (with S. Hemon and M. Santha),Symposium of Algo-rithmic Game Theory, 2008.

• Approximate validity of XML streaming data (with Cheng Huang and Jun Li), International Conference onWeb-Age Information Management, WAIM, 2008.

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Miklos Santha, Directeur de Recherche CNRS, LRI

EducationUniversite Paris-Sud, Orsay 1985 - 88Doctorat d’Etat in Computer ScienceThesis title: Contributions a l’etude des structures aleatoires et des methodes probabilistes

Universite Paris VII, Paris 1980 - 83Doctorat de 3e cycle (Ph.D.) in MathematicsAdvisor: Jacques SternThesis title: Contributions a l’etude de la hierarchie polynomiale relativisee

EmploymentCentre National de la Recherche Scientifique, Orsay 1988 - presentDirecteur de Recherche (Senior Researcher) in Computer Science

Universite Paris-Sud, Orsay 1985 - 88Maıtre de conferences (Assistant Professor) in CS

University of California, Berkeley 1983 - 85Research and Teaching Assistant in CS

Universite Paris VII, Paris 1980 - 83Research Assistant in Mathematics

Linguistical Institute of the Hungarian Academy, Budapest 1979 - 80Researcher in Linguistic

Research interestsQuantum computing, probabilistic algorithms, computational complexity

Ph.D. StudentsPh.D. Advisor in CS at the Universite Paris-Sud of 11 students between 1990 and 2007

Steering Committees1. “Fundamentals of Computation Theory” since 1999

2. “Quantum Information Processing” since 2002

3. “Symposium on Theoretical Aspects of Computer Science” since 2002.

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Program Committees1. 1st European Symposium on Algorithms, Bonn, 1993

2. 3rd European Symposium on Algorithms, Patras, 1995

3. 14th Symposium on Theoretical Aspects of Computer Science, Lubeck, 1997

4. 12th IEEE Conference on Computational Complexity, Ulm, 1997

5. 26th International Colloquium on Automata, Languages and Programming, Prague, 1999

6. 14th International Symposium on Fundamentals of Computation Theory, Malmo, 2003

7. 31st International Colloquium on Automata, Languages and Programming, Turku, 2004

8. 45th Annual IEEE Symposium on Foundations of Computer Science, Rome, 2004

9. 5th Erato Conference on Quantum Information Science, Tokyo, 2005

10. 9th Workshop on Quantum Information Processing, Paris, 2006 (PC Chairman)

11. 7th European Workshop on Quantum Information Processing and Communication, London, 2006

12. 2nd Asian Conference on Quantum Information Science, Kyoto, 2007

Selection of publications1. with U. V. Vazirani, Generating quasi-random sequences from semi-random sources, Journal of Computer

and System Sciences, 33, 1986, pp. 75-87.

2. with C. Wilson, Polynomial size constant depth circuits avec a limited number of negations, SIAM Journal ofComputing, Vol. 22, No. 2, pp. 294-302, 1993.

3. with G. Brassard and Claude Crepeau, Oblivious transfers and intersecting codes, IEEE Transactions onInformation Theory, Vol 42, No. 6, pp. 1769-1780, 1996.

4. with C. Durr, A decision procedure for unitary linear quantum cellular automata, SIAM J. of Computing, Vol.31, No. 4, pp. 1076–1089, 2002.

5. with W. van Dam, F. Magniez and M. Mosca, Self-Testing of universal and fault-tolerant sets of quantumgates, SIAM Journal of Computing, Vol. 37, No. 2, pp. 611–629, 2007.

6. with F. Magniez and M. Szegedy, Quantum algorithms for the triangle problem, SIAM Journal of Computing,Vol. 37, No. 2, pp. 413–424, 2007.

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