Quantum Neural Network (QNN) - Connecting Quantum and Brain with Optics - Yoshihisa Yamamoto NTT Physics & Informatics Laboratories NTT (2016) NTT (2019) Stanford (2014) 2K neurons, 4M synapses 4 neurons, 12 synapses Prototype NTT IR Day (Tokyo, September 26, 2019)

What problems to be solved? 2

Combinatorial Optimization Problems https://ja.storyblocks.com/stock- https://www.semanticscho image/smart-city-and-wireless- lar.org/paper/Filamentous communication-network- -supramolecular-peptide- abstract-image-visual-internet-of- drug-conjugates-Yang- things-mono-blue-tone-- Xu/a3062f178bde8f7b3156 roiwpowejgj044z2ev 309a3042e199f86cb5e7 Resource optimization in Lead optimization for discovery of wireless communication small molecule drug logistics peptide drug scheduling biocatalyst https://ja.wikipedia.org/wiki Compressed sensing (sparse coding) in Deep machine learning in https://iartificial.net/rede s-neuronales-desde-cero- Astronomy i-introduccion/ Self-driving cars Magnetic Resonance Imaging (MRI) Healthcare Computed Tomography (CT) Voice and image recognition 3

Lead Optimization Drug discovery: B iocatalyst discovery: Identify a group of compounds that Identify a group of proteins that can are attached most stably to a target protein. capture most stably a target compound. Protein Search space Search space ~ 10 46 (compounds) ~ 10 690 (proteins) Machine size Machine size ~ 4000 (neurons) ~ 60,000 (neurons) compound There are only 10 80 atoms in the observable universe! small molecule drug (6 sites/6 atomic species) Sampling by QNN Theoretical Boltzmann Histgram distribution Density of states Energy 4

Compressed Sensing (Sparse Coding) original data (N) observation (scattering) matrix observation data (M) MRI/CT Black Hole iteration Solve N 0 unknowns Identify non-zero components ( N 0 ) (inverse matrix computation) (support estimate) 𝑂 0 𝑂 Optimum QNN Τ (QNN) Recovery Efficiency a = QNN saturates the theoretical limit (Optimum) by deep compressed sensing. Approximate (Classical Computer) 5 Observation Efficiency 𝛽 = 𝑁 𝑂 Τ

Quantum Computing – Dream or Nightmare - 6

The Idea of Quantum Computing Superposition 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. first qubit second qubit N -th qubit 1 1 ⊗ 1 2 ∙∙∙∙∙∙∙∙∙∙∙∙⊗ 1 ȁ ۧ 0 + ȁ ۧ ȁ ۧ 0 + ȁ ۧ ȁ ۧ 0 + ȁ ۧ 1 1 1 𝑂 2 2 2 1 2 𝑂 ȁ ۧ 0 1 ȁ ۧ 0 2 ∙∙∙ ȁ ۧ 0 𝑂 + ȁ ۧ 0 1 ȁ ۧ 0 2 ∙∙∙ ȁ ۧ 1 𝑂 ∙∙∙∙∙∙∙∙∙∙∙∙ +ȁ ۧ 1 1 ȁ ۧ 1 2 ∙∙∙ ȁ ۧ = 1 𝑂 state 1 State 2 N state 2 N qubits can represent 2 N different states simultaneously, while N classical gates can represent only one state. 2 N outputs Quantum computer Classical computer (superposition) input 1 input 1 output 1 ① ② ③ input 2 Simultaneous Read out? input 2 output 2 computation over 2 N inputs input 2 N output 2 N input 2 N N qubits compute a cost function simultaneously for 2 N input states. Single Run Brute Force Search 7

Weakness of Quantum Computing Time-to-Solution by an ideal quantum computer Grover (optimum) algorithm (1997) for the Combinatorial Optimization Problem (Ising model) Probability =1 Problem Size N (bits) Time-to-Solutions T s 4 x 10 -3 s 20 Probability Amplitude 6 x 10 2 s 50 2 𝑂 repetitions 2 x 10 10 s → exponential scaling 100 (~700 years) Linear increase of 6 x 10 17 (s) (~20B years) 150 1 amplitude by 1 Amplitude 2 𝑂 2 𝑂 An ideal quantum computer, with no 1 2 3 Optimum solution 2 N decoherence, no gate error and all- to-all qubit coupling with 1 ns gate Solution candidates time, cannot find a solution even for Optimum algorithm is still highly inefficient. small-size combinatorial optimization problems. 8

NTT’s Vision - Let’s try a fundamentally different approach - 9

Quantum Neural Network (QNN) From quantum only to quantum and classical simultaneously Optical parametric oscillator @ 300 K Artificial two-level atom @ 10 mK Quantum Quantum Classical Classical above Digital Digital threshold https://web.physics.ucsb.edu/~ https://optoelectronics.ece. martinisgroup/photos/SurfaceCo below ucsb.edu/sites/default/files/ deThreshold.jpg Analog Analog 2017-06/C1007_0.pdf threshold Superconducting Thin-Film periodically circuit poled LiNbO 3 waveguide From local (sequential) computation to global (parallel) computation Time Quantum computer Quantum neural network 10

Why do we need classical resources ? - Irreversible Decision Making and Exponential Amplitude Amplification - Spontaneous symmetry breaking Yoichiro Nambu Exponential amplitude amplification Quantum correlation induced in optical parametric oscillators collective symmetry breaking for decision making Probability =1 above threshold (OPO) 1 (OPO) 2 (OPO) N Probability Amplitude Exponential increase of amplitude at No repetition optical parametric required oscillator (DOPO) threshold ȁ ۧ 1 𝑂 ȁ ۧ 1 1 ȁ ۧ 0 2 1 Amplitude below threshold 2 𝑂 This critical phenomenon is completed in a time interval of a photon lifetime 2 N Optimum solution 1 2 3 ( μ sec ~ msec ) All candidates This process is triggered by quantum correlation and completed by classical effects. 11

Time-to-Solution for the Combinatorial Optimization Problems (Ising model) Experimental Quantum Heuristic Machines Theoretical Problem Size Quantum * ** *** Quantum Computing Quantum Computing Quantum Annealing Neural Network 4 x 10 -3 (s) 6 x 10 2 (s) 1.1 x 10 -5 (s) 1.0 x 10 -4 (s) N = 20 ~10 7 6 x 10 2 (s) 2.0 x 10 3 (s) 3.7 x 10 -4 (s) N = 55 --- ~10 7 2 x 10 10 (s) 2.5 x 10 -3 (s) N = 100 --- --- ( ～ 700 years) 6 x 10 17 (s) 5.4 x 10 -2 (s) N = 150 --- --- ( ～ 20B years) * 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) 12 12

NTT Laboratories - Past 40 years and next 40 years - 13

Basic Research on Quantum Computing at NTT Laboratories – Past 40 years – 1980 1990 2000 2010 2020 1979 1986 1988 1995 2002 2014 2016 2019 Optical parametric Coherent optical Differential Phase Scalable oscillator with Shift (DPS) quantum communications quantum measurement- communication proposed neural network feedback proposed proposed demonstrated Measurement- Coherent Ising machine Squeezed vacuum state Benchmark induced control of (CIM) pulses from PPLN-OPO against QC quantum states and QA 14

Basic Research on Quantum Computing at NTT Laboratories - Next 40 Years - Next Frontier Industry-Academia Open Laboratory 15

Future Prospect 16

A human brain is already a quantum computer? A. Levina et al., Nat. Phys. 3, 857 (2007); D. R. Chialvo et al., Nat. Phys. 6, 744 (2010) 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) Frequency Frequency Correlation Length ( k ) Correlation Length ( k ) Human Brain Ising Spin Network at Default Mode (f-MRI data) at Phase Transition Point 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). 17

Scalability of Three Quantum Machines and Human Brain Number of Neurons (Spins) Number of Synapses Number of Synapses Number of Neurons Problem size Computational Capability 19

Thank you NTT Physics & Informatics Laboratories https://ntt-research.com/phi/ NTT Basic Research Laboratories https://www.brl.ntt.co.jp/e/index.html 19

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