Quantum InformationScience

John Preskill30 Oct 2009

???Putting Weirdnessto Work:

Caltech’s Information Science

and Technology Initiative

Bruck Murray

“Within the next 10-20 years, information will be a unifying, core intellectual theme spanning physical sciences, biological sciences, social sciences, and engineering. IST will fundamentally transform the research and educational environment at Caltech and other universities around the world.”

IST Planning Committee, 2002

Annenberg Center for Information Science

and Technology

Bruck Murray

SchröderGorilla

Caltech and Information Science

Nanotechnology: there’s plenty of room at the bottom.

Mead

Feynman

Hopfield

CNS: How does the brain compute?

VLSI: New paradigm for the semiconductor industry.

Caltech and Information Science

As we run out of “room at the bottom,” the world needs visionary ideas about how physical systems can store and process information. Providing those ideas, and training the people who will put them into practice, is part of the mission of IST.

Mead

Feynman

Hopfield

Turing

Planck

Shannon

Quantum Information Science

Quantum physics, information theory, and computer science are among the crowning intellectual achievements of the 20th century.

Quantum information science is an emerging synthesis of these themes, which is providing important insights into fundamental issues at the interface of computation and physical science, and may guide the way to revolutionary technological advances.

Information

is encoded in the state of a physical system.

quantum

Information

is encoded in the state of a system.

Put

to work!

Quantum Entanglement

classically correlated socks quantumly correlated photons

• There is just one way to look at a classical bit (like the color of my sock), but there are complementary ways to observe a quantum bit (like the polarization of a single photon). Thus correlations among qubits are richer and much more interesting than correlations among classical bits.

• A quantum system with two parts is entangled when its joint state is more definite and less random than the state of each part by itself. Looking at the parts one at a time, you can learn everything about a pair of socks, but not about a pair of qubits!

The quantum correlations of many entangled qubits cannot be easily described in terms of ordinary classical information. To give a complete classical description of one typical state of just a few hundred qubits would require more bits than the number of atoms in the visible universe!

It will never be possible, even in principle to write down such a description.

We can’t even hope to describe the state of a few hundred qubits in terms of classical bits.

As Feynman first suggested in 1981, a computer that operates on qubits rather than bits (a quantum computer) can perform tasks that are beyond the capability of any conceivable digital computer!

Finding Prime Factors

1807082088687 4048059516561 64405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

? ?

An example of a problem that is hard for today’s supercomputers: finding the factors of a large composite number. Factoring e.g. 500 digit numbers will be intractable for classical computers even far into the future.

Finding Prime Factors

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39685999459597454290161126162883786067576449112810064832555157243

45534498646735972188403686897274408864356301263205069600999044599

But for a quantum computer, factoring is not much harder than multiplication! The boundary between the problems that are “hard” and the problems that are “easy” is different in a quantum world than a classical world.

Shor

Jeff KimblePhysics

Leonard SchulmanComputer Science

John PreskillPhysics

CENTER FOR THE PHYSICS OF INFORMATION

Gil RefaelPhysics

Alexei KitaevPhysics and Computer Science

Thanks!

IQI geography

Annenberg(IST)

Jorgensen

Steele

Lauritsen

SloanAnnex

Annenberg Center for Information Science

and Technology

Bruck Murray

SchröderGorilla

Hallgren

Terhal

BaconDuanDohertyNayak

VidalHayden Leung

Shi Geremia

Bose Bravyi

Verstraete Wocjan

Former IQI Postdocs now in faculty positions elsewhere

Childs

Raussendorf

Ardonne Zhang Poulin Reichardt

Penn State

IBM

U. Wash.MichiganQueenslandWaterloo

QueenslandMcGill Waterloo

Michigan UNM

London IBM

Vienna U. Central Fla

Former IQI Postdocs now in faculty positions elsewhere

Waterloo

UBC

Nordita Hong Kong Sherbrooke Waterloo

Quantum Information Challenges

And …what are the implications of these ideas for basic physics?

Cryptography

Privacy from physical principles

Hardware

Toward scalable devices

QuantumComputer

Error correction

Reliable quantum computers

Noise

Algorithms

What can quantum computers do?

| | ( )x G

x f x

But .. what does it have to do with information?

Perona

Since 1997: A physics course that includes …

Complexity, algorithms, data compression, channel capacity, cryptography and security, error-correcting codes, fault tolerance, …

whole > (parts)

Condensed matter physics

Emergent phenomena: the collective behavior of many particles cannot be easily guessed, even if we have complete knowledge of how the particles interact with one another.

Entangled quantum many-particle systems have an enormous capacity to surprise and delight us.

In a nutshell:

Fractional quantum Hall state High temp. superconductor Crystalline material

Vidal

Efficient classical simulation of quantum systems with bounded entanglement

In general, there is no succinct classical description of the quantum state of a system of n qubits. But suppose, e.g., for qubits arranged in one dimension, that for any way of dividing the line into two segments, the strength of the quantum correlation (the amount of entanglement) between the two parts is bounded above by a constant, independent of n.

Vidal showed that in that case a succinct description is possible, with O(n) parameters rather than 2n, and that the description can be easily updated as the state evolves (if the interactions are local).

This makes precise the idea that entanglement is the source of a quantum computer’s power: if the quantum computer does not become highly entangled, it can be efficiently simulated by a classical computer.

Furthermore, in one-dimensional systems with local interactions, the entanglement increases no more rapidly than log n, and an efficient classical simulation of real time evolution is possible.

Universal properties of entanglementFor the ground state of a large two-dimensional quantum system, consider the entanglement of a disk (circumference L) with the rest of the system. For a system with a nonzero energy gap, the entanglement is:

E L

LThe universal additive term, the topological entanglement entropy, is a global feature of the many-body quantum entanglement, characterizing the topological order of the gapped two-dimensional system. There is a simple formula for the universal constant , in terms of the properties of the particle excitations of the system.

PreskillKitaev

Term proportional to L, arising from short distance fluctuations near the boundary, is nonuniversal.

Additive correction is universal (independent of geometry and microscopic details).

How fast does information escape from a black hole?Hayden Preskill

Alice

black holeBob

Black holes are (we believe) efficient quantum information processors. How long do we have to wait for information absorbed by a black hole to be revealed in its emitted Hawking radiation? We have recently reconsidered this question using new tools from quantum information theory.

Our (tentative) conclusion is that the retention time can be surprisingly short. The analysis uses the theory of quantum error-correcting codes and quantum circuits.

strongly mixing unitary

maximalentanglement

Alice’s qubits

Bob decodes

blackhole

blackhole

radi

atio

n

radiation

John Preskill (Ph)Jeff Kimble (Ph)Kerry Vahala (APh)

Steering Committee

Mike Cross (Ph)Jim Eisenstein (Ph/APh)Alexei Kitaev (Ph/CS)Oskar Painter (APh)Demetri Psaltis (EE)

Gil Refael (Ph)Dave Rutledge (EE)Michael Roukes (Ph/APh)Erik Winfree (CS/CNS)Amnon Yariv (APh/EE)Etc.

CPI is dedicated to the proposition that physical science and information science are interdependent and inseparable. Our research aims, on the one hand, to foster physical insights that can pave the way for revolutionary new information technologies, and, on the other hand, to stimulate new ideas about information that can illuminate fundamental issues in physics and chemistry.

Warwick Bowen (Kimble): Strong coupling in cavity quantum electrodynamicsYounkyu Chung (Rutledge): High power 80 GHz amplifiers for wireless JM Geremia (Mabuchi): Stochastic feedback control & high precision measurement Tobias Kippenberg (Vahala): Optical driving of microcavity oscillatorsPaul Rothemund (Winfree): Complex patterns from DNA self-assemblyJacob Scheuer (Yariv): Ring resonators for all-optical nonlinear devicesFrank Verstraete (Preskill): Efficient simulation of highly correlated quantum systems

Tal Carmon (Vahala): Micron scale on-chip photonic devicesMartin Centurion (Psaltis): Nonlinear optical processing via defocusingBarak Dayan (Kimble): Strong coupling of atoms to toroidal optical resonatorsMatt LaHaye (Roukes): Quantum limited measurements with nanoelectromechanicsSung Ha Park (Winfree): Algorithmic self-assembly with low error rateMason Porter (Cross): Bose-Einstein condensates and nonlinear dynamics

Eddy Ardonne (Kitaev): Braiding properties of two-dimensional quasiparticlesHui Deng (Kimble): Toward scalable quantum networksGhislain Granger (Eisenstein): Nonabelian statistics in fractional quantum Hall statesMani Hossein-Zadeh (Vahala): Radiation pressure instability in toroidal resonatorsDavid Poulin (Preskill): Quantum belief propagation and many-body physics Kartik Srinivasan (Painter): Solid-state cavity quantum electrodynamics

Scott Papp (Kimble): Information processing with cold atomic gasesAvi Zadok (Yariv): Secure classical key distribution based on laser oscillationsDarrick Chang (Preskill): Optical levitation of nanoscale mechanical systems Hansuek Lee (Vahala): Low loss waveguides and micro-resonators for optical integrated circuits

CPI Postdoctoral Scholars

Coherent manipulation of encoded information

laser

Interacting optical and mechanical modes of silica microtoroids. Hossein-Zadeh (Vahala)

Cavity QED with semiconductor quantum dots embedded in micro-disks. Srinivasan (Painter)

CPB

ResonatorResonator

Gate

SETCPBGate

SETGate

CPB and NEMS Sample1m CPB

ResonatorResonator

Gate

SETCPBGate SET

Gate

CPB and NEMS Sample1m

Coupling a GHz mechanical resonator to a Cooper-pair box. LaHaye (Roukes & Schwab)

Mapping entangle-ment into and out of quantum memory. Deng (Kimble)

=1

Toward qubits in quantum Hall systems. Granger (Eisenstein)

Quantum Information Science

Atomic-MolecularOptical Physics

CondensedMatter Physics

Exotic QuantumSystems!

Exotic QuantumSystems!

Eisenstein Roukes Schwab

Preskill Kitaev Schulman

Kimble Painter Vahala

All-Star All-Star

Refael Motrunich Fisher

Caltech and quantum information – looking ahead

• Quantum information science did not exist 30 years ago. There will be many more surprises in the next 30 years.

• Caltech has a strong leadership position that should be nurtured.

• The convergence of quantum information, condensed matter, and atomic-molecular-optical physics will continue, becoming one of Caltech’s great strengths.

• PMA and EAS will share an increasing interest in quantum devices (broadly interpreted), e.g., coherent light, correlated electrons, quantized mechanical motion, control of quantum effects, etc.

As always, our future success hinges on finding and recruiting talented and visionary young people.