quantum neural network (qnn) ·...
TRANSCRIPT
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Quantum Neural Network (QNN) - Connecting Quantum and Brain with Optics -
NTT (2016)
2K neurons, 4M synapses NTT (2019)
Prototype
Yoshihisa YamamotoNTT Physics & Informatics Laboratories
NTT IR Day (Tokyo, September 26, 2019)
Stanford (2014)
4 neurons, 12 synapses
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What problems to be solved?
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Resource optimization in
wireless communication
logistics
scheduling
Lead optimization for discovery of
small molecule drug
peptide drug
biocatalyst
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Combinatorial Optimization Problems
Compressed sensing (sparse coding) in
Astronomy
Magnetic Resonance Imaging (MRI)
Computed Tomography (CT)
Deep machine learning in
Self-driving cars
Healthcare
Voice and image recognition
https://iartificial.net/redes-neuronales-desde-cero-i-introduccion/
https://ja.wikipedia.org/wiki
https://www.semanticscholar.org/paper/Filamentous-supramolecular-peptide-drug-conjugates-Yang-Xu/a3062f178bde8f7b3156309a3042e199f86cb5e7
https://ja.storyblocks.com/stock-image/smart-city-and-wireless-communication-network-abstract-image-visual-internet-of-things-mono-blue-tone--roiwpowejgj044z2ev
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Lead Optimization
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Biocatalyst discovery: Identify a group of proteins that can
capture most stably a target compound.
Search space
~ 10690 (proteins)
Machine size
~ 60,000 (neurons)
Protein
Drug discovery: Identify a group of compounds that
are attached most stably to a target protein.
Search space
~ 1046 (compounds)
Machine size
~ 4000 (neurons)compound
There are only 1080 atoms in the observable universe!
Energy
Sampling by QNN
Theoretical Boltzmann
distribution
Den
sity
of
state
s H
istg
ram
small molecule drug (6 sites/6 atomic species)
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Identify non-zero components (N0)(support estimate)
observation data (M)
observation (scattering) matrix
original data (N)
Compressed Sensing (Sparse Coding)
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Black Hole MRI/CT
Solve N0 unknowns (inverse matrix computation)
iteration
QNN saturates the theoretical limit (Optimum)
by deep compressed sensing.
Optimum
(QNN)
Approximate
(Classical Computer)
QNN
Rec
ove
ry E
ffic
ien
cy a=
Τ𝑁0𝑁
Observation Efficiency 𝛼 = Τ𝑀 𝑁
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Quantum Computing – Dream or Nightmare -
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The Idea of Quantum Computing
① ② ③
Classical computer
output 1
output 2
output 2N
input 1
input 2
input 2N
Brute Force Search
Quantum computer
N qubits compute a cost function
simultaneously for 2N input states.
Simultaneous
computation
over 2N inputs
Read out?
input 1
input 2
input 2N
2N outputs(superposition)
Single Run
Superposition
1
2ȁ ۧ0 + ȁ ۧ1 1⊗
1
2ȁ ۧ0 + ȁ ۧ1 2 ∙∙∙∙∙∙∙∙∙∙∙∙⊗
1
2ȁ ۧ0 + ȁ ۧ1 𝑁
=1
2𝑁ȁ ۧ0 1ȁ ۧ0 2 ∙∙∙ ȁ ۧ0 𝑁 + ȁ ۧ0 1ȁ ۧ0 2 ∙∙∙ ȁ ۧ1 𝑁 ∙∙∙∙∙∙∙∙∙∙∙∙ +ȁ ۧ1 1ȁ ۧ1 2 ∙∙∙ ȁ ۧ1 𝑁
state 2state 1 State 2N
first qubit second qubit N-th qubit
A gate voltage in classical computer is either 0(V) or 1(V), while qubit in quantum computer is
simultaneously l0> state and l1> state.
N qubits can represent 2N different states simultaneously, while N classical gates can
represent only one state.
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Weakness of Quantum Computing
Optimum solution1 2 3 2N
Solution candidates
Probability =1
Amplitude 1
2𝑁
Linear increase of amplitude by
1
2𝑁
2𝑁 repetitions→ exponential scaling
Pro
bab
ilit
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litu
de
Grover (optimum) algorithm (1997)
Optimum algorithm is still highly inefficient.
Time-to-Solution by an ideal quantum computer
for the Combinatorial Optimization Problem
(Ising model)
Problem Size N (bits) Time-to-Solutions Ts
20 4 x 10-3 s
50 6 x 102 s
100 2 x 1010 s (~700 years)
150 6 x 1017 (s) (~20B years)
An ideal quantum computer, with no
decoherence, no gate error and all-
to-all qubit coupling with 1 ns gate
time, cannot find a solution even for
small-size combinatorial
optimization problems.
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NTT’s Vision
- Let’s try a fundamentally different approach -
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Quantum Neural Network (QNN)
From quantum only to quantum and classical simultaneously
Quantum Classical
Digital
Analog
Quantum Classical
Digital
Analog
above threshold
below threshold Thin-Film periodically
poled LiNbO3 waveguide
Superconducting
circuit
Optical parametric oscillator @ 300 KArtificial two-level atom @ 10 mK
Quantum computer Quantum neural network
From local (sequential) computation to global (parallel) computation
Time
https://optoelectronics.ece.ucsb.edu/sites/default/files/2017-06/C1007_0.pdf
https://web.physics.ucsb.edu/~martinisgroup/photos/SurfaceCodeThreshold.jpg
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Why do we need classical resources ? - Irreversible Decision Making and Exponential Amplitude Amplification -
Yoichiro Nambu
This process is triggered by quantum correlation and completed by classical effects.
Quantum correlation induced
collective symmetry breaking
for decision making
This critical phenomenon is completed
in a time interval of a photon lifetime
(μsec ~ msec)
(OPO)1 (OPO)2 (OPO)N
above threshold
below threshold
ȁ ۧ1 𝑁ȁ ۧ0 2ȁ ۧ1 1
Optimum solution
Probability =1
Exponential amplitude amplification
in optical parametric oscillators
1 2 3 2N
Exponential increase of amplitude at optical parametric oscillator (DOPO) threshold
Amplitude 1
2𝑁
All candidates
No repetitionrequired
Pro
bab
ilit
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mp
litu
de
Spontaneous symmetry breaking
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Problem Size
Theoretical
Quantum
Computing
Experimental Quantum Heuristic Machines
Quantum Computing Quantum AnnealingQuantum
Neural Network
N = 20 4 x 10-3 (s) 6 x 102 (s) 1.1 x 10-5 (s) 1.0 x 10-4 (s)
N = 55 6 x 102 (s) --- 2.0 x 103 (s) 3.7 x 10-4 (s)
N = 1002 x 1010 (s)
(~700 years)--- --- 2.5 x 10-3 (s)
N = 1506 x 1017 (s)
(~20B years)--- --- 5.4 x 10-2 (s)
* Theoretical limit (no decoherence, no gate error, all-to-all connections, 1 ns gate time)
** Rigetti Quantum Computer (Quantum Approximate Optimization Algorithm, Dec. 2017)
*** D-WAVE 2000Q @ NASA Ames (March 2019)
* *****
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Time-to-Solution for the Combinatorial Optimization Problems (Ising model)
~107
~107
12
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NTT Laboratories
- Past 40 years and next 40 years -
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1980 1990 2000 2010 2020
Basic Research on Quantum Computing at NTT Laboratories
– Past 40 years –
Coherent optical
communications
proposed
1979
Measurement-
induced control of
quantum states
1986
Optical parametric
oscillator with
measurement-
feedback proposed
1988
Differential Phase
Shift (DPS) quantum
communication
proposed
2002
Scalable
quantum
neural network
demonstrated
2016
Benchmark
against QC
and QA
2019
Squeezed vacuum state
pulses from PPLN-OPO
1995
Coherent Ising machine
(CIM)
2014
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Basic Research on Quantum Computing at NTT Laboratories- Next 40 Years -
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Industry-Academia Open LaboratoryNext Frontier
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Future Prospect
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A human brain is already a quantum computer?
At the oscillation threshold of Ising spin networks, 1. spin-to-spin correlation occurs across all scales (→ communication)
2. randomness is maximum (→ information storage)
3. responsibility is maximum (→ signal amplification)
Ising Spin Network
at Phase Transition Point
Human Brain
at Default Mode (f-MRI data)correspondence
How large number of neurons collectively interact to produce emergent
properties like cognition and consciousness?
Editorial: John Beggs, Phys. Rev Lett. 114 220001 (2015).
A. Levina et al., Nat. Phys. 3, 857 (2007); D. R. Chialvo et al., Nat. Phys. 6, 744 (2010)
Fre
qu
en
cy
Fre
qu
en
cy
Correlation Length (k) Correlation Length (k)
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Scalability of Three Quantum Machinesand Human Brain
Number of Neurons Problem size Number of Synapses
Computational Capability
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Number of Neurons (Spins) Number of Synapses
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Thank you
NTT Physics & Informatics Laboratories
https://ntt-research.com/phi/
NTT Basic Research Laboratories
https://www.brl.ntt.co.jp/e/index.html