From quantum hardware to quantum AI · 15-11-2018 · Programmable matter is matter which has the...
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CLASSICAL BIT vs QUBIT Computation as physical process Concept of programmable matter Classical neural network Distance between quantum states Quantum algorithms Quantum Neural Networks From quantum hardware to quantum AI School of Electrical and Electronic Engineering University College Dublin Krzysztof Pomorski, Panagiotis Giounanlis, Elena Blokhina, Robert Staszewski November 15, 2018 Krzysztof Pomorski From quantum hardware to quantum AI
Transcript of From quantum hardware to quantum AI · 15-11-2018 · Programmable matter is matter which has the...
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
From quantum hardware to quantumAI
School of Electrical and Electronic EngineeringUniversity College Dublin
Krzysztof Pomorski, Panagiotis Giounanlis,Elena Blokhina, Robert Staszewski
November 15, 2018
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
CLASSICAL BIT vs QUBIT
Computation as physical process
Concept of programmable matter
Classical neural network
Distance between quantum states
Quantum algorithms
Quantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Classical computation vs quantum computation
CLASSICAL LOGIC:I Sharp Logic [Boolean 0 or 1 State]I Fuzzy Logic [Based on Continous State between 0 and 1]
QUANTUM LOGIC:I Logic BASED on qubits (|ψ >= α|0 > +β|1 >), where α andβ are complex valued with condition 1 = |α|2 + |β|2 whatgives α = cos(Θ)e iγ , β = sin(Θ)e iδ
It is important to note that qubit state can be always written as
|ψ >= α
(01
)+ β
(10
)= e iγ [cos(Θ)
(01
)+ sin(Θ)e i(δ−γ)
(10
)].
(1)Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Computation as physical process
In all cases the computation is the results of physical evolution ofthe given system that is implemented in some technology. At firststage we set certain initial conditions of the system and we allowthem to evolve what is equivalent of performing the algorithmicsteps. After certain time system is achieving its final state. Thenwe perform the readout or measurement on certain sections ofphysical system that we name registors.In such way we determinethe computational result. System can evolve in dissipative andsometimes in non-dissipative way so there is presence of frictionand entropy is usually increasing. By delivering energy to thesystem the information entropy might also decrease. For examplefiltering the image might bring lower entropy of the picture once itis being processed. It is valid for classical and quantum computers.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Concept of programmable matter
Programmable matter is matter which has the ability to change itsphysical properties (shape, density, moduli, conductivity, opticalproperties, etc.) in a programmable fashion, based upon user inputor autonomous sensing. Programmable matter is thus linked to theconcept of a material which inherently has the ability to performinformation processing.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Braitenberg vehicles
Adaptability and Diversity in Simulated Turn-taking BehaviourHiroyuki Iizuka Takashi Ikegami, → Quantum Braitenberg vehicleswith use of time-depedent Schroedinger equation+finite statemachine??? as next stage towards Q-Alife???? Or shall weconsider the quantum ants ???
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Ikegami Braitenberg vehicles
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
General defintion of AI
From that point of view AI or embodied AI is also physicalevolution with use of concept of programmable matter. AI isprogrammable matter that is able to interact with enviroment indynamical way. Embodied AI is special version of AI where theinteraction of enviroment and artificial evolution brings theemergence of new properties.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
For a single neuron z depending on x = (x1, . . . , xn), themathematical operation can thus be visualized as it is depicted.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Figure: Non-linear activation functions used in Artificial Neural Networks.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Schroedinger equation
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Quantum entanglement
Quantum state collapses after measurement.|ψ >= 1
2 (| ↑↓> ±| ↓↑>), → |ψ1 >= (| ↑↓>) [collapse ofwavefunction after measurement]!!!!
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Key features of Quantum Mechanics and QuantumTechnologies
1. Massive parallelism occurs in isolated quantum system2. Non-sharp trajecories and lack of full determinism.3. Quantum metrology and quantum sensing is the bestperception.[However the object under observation is changing what alsoaffects the measurement apparatus]4. No-cloning and no-deleting theorem.5. Quantization of physical quantities as energy, momentum, etc ...6. Non-locality as occurence of entanglement that is spooky actionon the distance.7. Occurence of teleportation.8. Some analogies of QM with Classical Statistical Mechanics .9. Quantum technologies are hardly accessible and require very lowtemperatures as 15mK...10. Wave-particle duality.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
During a lecture in the early 1980s, Richard Feynman proposed theconcept of simulating physics with a quantum computer (Feynman1982). He postulated that by manipulating the properties ofquantum mechanics and quantum particles one could develop anentirely new kind of computer, one that could not be described bythe classical theory of computation with Turing machines. Naturedoes not explicitly perform the calculations to determine the speedof a ball dropped from a tall building; it does so implicitly.Extending this line of thinking, Feynman wondered if one couldharness the complex calculations nature performs intrinsically inquantum mechanics to design a computer with morecomputational power.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
General scheme of quantum neural network
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Comparison of Wavefunction vs ANN
As from [4].Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
As from [4].
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Quantum neural network in coupled q-dots
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Concept of fidelity and quantum fidelity
Given two random variables X, Y with values (1...n) andprobabilities p = (p1...pn) and q = (q1...qn). The fidelity of X andY is defined to be the quantity
F (X ,Y ) =∑
i
√piqi . (2)
Given two density matrices ρ and σ, the fidelity is defined by[2]
F (ρ, σ) =
(Tr√√
ρσ√ρ
)2
. (3)
There are many other measures of the distance!!!!
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Bures distance
Fidelity can be used to define metric on the set of quantum states,so called Bures distance:
DB(X ,Y ) = 2− 2F (ρ, σ). (4)
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
Classical vs quantum annealing
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
In most general case the eigenstate of quantum system can bewritten in the following way at given time instant t.
|ψ(t) >= a0(t)|0(t) > +a1(t)|1(t) >< 1(t)|+ ..an1(t)|n1(t) > +
+(
∫ q2(t)
q1(t)g(e1, t)de1)|e1(t) > . (5)
The coefficients a0, .., an fulfill the normalization condition
1 = |a0|2 + ..|an|2 +∫ q2(t)
q1(t) |g2|de1. Dynamics of quantum state
gives
i~d
dt|ψ(t) >= H(t)|ψ(t) >= E (t)|ψ(t) > . (6)
and can be written in discrete form as
|ψ(t + ∆t) >= |ψ(t) > +−i∆t
~(H(t + ∆t)|ψ(t) >). (7)
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
H(t) = E0(t)|0(t) >< 0(t)|+ E1(t)|1(t) >< 1(t)|+ ..+
+En(t)|n(t) >< n(t)|+∫ q2(t)
q1(t)f (e1, t)de1|e1(t) >< e1(t)|. (8)
a0(t + ∆t) = (< 0(t + dt)|0(t) > a0(t)+ < 0(t + dt)|1(t) > a1(t) + ..
+ < 0(t + dt)|n(t) > an(t)) + ..
a1(t + ∆t) = (< 1(t + dt)|0(t) > a0(t)+ < 1(t + dt)|1(t) > a1(t) + ..
+ < 1(t + dt)|n(t) > an(t)) + ..
..
an(t + ∆t) = (< n(t + dt)|0(t) > a0(t)+ < n(t + dt)|1(t) > a1(t) + ..
+ < n(t + dt)|n(t) > an(t)) + ..
(9)Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
In 2-body systemH = − ~2
2m ([ d2
dx21× I ] + [I × d2
dx22
]) + e2
4πε0|x1−x2| + V1(x1, t) + V2(x2, t)
with ψ(x1, x2) = ψ(x0 + i∆x , x0 + j∆x) = ψi ,j and Euler schemefor 2nd derivative. Initial state isψ(x , y , t0) =
∑i ,j ai ,jψi (x1, t0)ψj (x2, t0)),
∑i ,j |ai ,j |2 = 1 is linear
combination of non-interacting free particles with Ei ,Ej energies.
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
(− ~2
2m
d2
dx2A
+ λ
∫ +∞−∞ e2ψB(x)ψ†B(x)dx
4πε0|xA − x |+ VA(xA))ψA(xA) = EAψA(xA)
(− ~2
2m
d2
dx2B
+ λ
∫ +∞−∞ e2ψA(x)ψ†A(x)dx
4πε0|xB − x |+ VB(xB))ψB(xB) = EBψB(xB)
∫ +∞
−∞ψ†A(xA)HB−eff ψB(xA)dxA +
+
∫ +∞
−∞ψ†B(xB)HB−eff ψB(xB)dxB =< Htotal >
Krzysztof Pomorski From quantum hardware to quantum AI
CLASSICAL BIT vs QUBITComputation as physical processConcept of programmable matter
Classical neural networkDistance between quantum states
Quantum algorithmsQuantum Neural Networks
References
[1]. Tommaso Toffoli, Norman Margolus, Programmable matter: Concepts and realization, Physica D: NonlinearPhenomena, Vol.47, 1991 https://www.sciencedirect.com/science/article/pii/016727899190296L
[2]. https://medium.com/xanaduai/making-a-neural-network-quantum-34069e284bcf
[3]. http://www.studioflorian.com/projekty/252-monika-rafajova-programmable-matter
[4]. Alexandr A. Ezhov and Dan Ventura, Quantum neural networkshttp://axon.cs.byu.edu/papers/ezhov.fdisis00.pdf
[5]. Richard Jozsa, Fidelity for Mixed Quantum Stateshttps://www.tandfonline.com/doi/abs/10.1080/09500349414552171?journalCode=tmop20
[6]. HOW TO MEASURE FIDELITY BETWEEN TWO MIXED QUANTUM STATES?https://perimeterinstitute.ca/videos/how-measure-fidelity-between-two-mixed-quantum-states
[7]. Wei Hu, Towards a Real Quantum Neuron https://file.scirp.org/pdf/NS_2018031517004350.pdf
[8]. D. Deutsch, Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer[9]. Universal quantum perceptron as efficient unitary approximators E. Torrontegui and J.J.Garcıa-Ripoll[10]. Carlos Pedro Goncalves, Quantum Neural Machine Learning: Backpropagation and Dynamicshttps://neuroquantology.com/index.php/journal/article/view/1008/814
[11]. https://arxiv.org/pdf/1512.01141.pdf
[12]. The quest for a Quantum Neural Network-Maria Schuld, Ilya Sinayskiy, Francesco Petruccione[13]. Feynman, R.P. Simulating physics with computers, Int. J.Theor.Phys. 21(1982)467-488.[14]. Feynman, R.P. Quantum Mechanical Computers, Found. Phys. 16(1986)507-531.[15]. Alexandre M. Zagoskin et al. , How to test the “quantumness” of a quantum computer?[16]. http://www.sciencemag.org/news/2016/12/
scientists-are-close-building-quantum-computer-can-beat-conventional-one
Krzysztof Pomorski From quantum hardware to quantum AI
