Feature Articles: Establishment of NTT Research, Inc. toward the Strengthening and Globalization of Research and Development Mission of Physics & Informatics Laboratories Yoshihisa Yamamoto Abstract At the Physics & Informatics Laboratories (PHI Labs) of NTT Research, Inc., we explore a new prin- ciple that will bring about a revolution in information processing technology in the interdisciplinary area between quantum physics and brain science, and it is here where we have positioned our research field. We will focus on quantum-classical crossover physics and critical phenomena in neural networks. We will concentrate, in particular, on optical implementation as a means of achieving a simple, elegant, and practical implementation of a computer that is based on this new principle, specifically on the optical parametric oscillator that can achieve quantum neural networks at room temperature. This article intro- duces the concepts, technologies, and target applications making up this research field at PHI Labs. Keywords: combinatorial optimization problem, quantum neural network, optical parametric oscillator 1. Quantum neural networks using optical waves for practical use) in 1968 by Stephen Harris parametric oscillators and Robert Byer of Stanford University [2]. The foundation of optical communication technol- The development of new oscillators for generating ogy, which blossomed in the 20th century, was the coherent electromagnetic waves and the expansion of laser, but it is our future vision that the foundation of their application fields has a history marked by a optical information processing technology of the 21st rivalry between oscillators based on two different century will be the optical parametric oscillator. This principles. In electrical engineering terms, one is a type of parametric oscillator behaves like an analog negative-resistance oscillator requiring no pump- device with strong quantum properties in the pump source coherence, and the other is a nonlinear reac- region below an oscillation threshold and like a digi- tance oscillator requiring coherent pump waves. The tal device with strong classical properties in the pump development of oscillators for various frequency region above the threshold. As described below, bands began with the emergence of negative-resis- future information processing technology will require tance oscillators that are easy to achieve. This was both quantum computing resources and classical followed by the development of nonlinear reactance computing resources, and the optical parametric oscillators that generate a coherent wave with less oscillator is practically the only device that can noise. simultaneously achieve this dual quantum-classical The development of optical oscillators covering a nature at room temperature. broad wavelength band from ultraviolet to infrared is We have been researching the neural networks no exception to this historical rivalry. A laser, which using optical parametric oscillators as neurons and is an optical negative-resistance oscillator, was devel- using such a configuration in an attempt to solve oped in 1960 through the work of Theodore Maiman combinatorial optimization problems and quantum of Hughes Research Laboratories [1]. This was fol- many-body problems that have posed a challenge to lowed by the development of an optical nonlinear the modern computer [3] (Fig. 1). Regarding another reactance oscillator as an optical parametric oscillator element (synapse connections) making up a neural (in particular, an oscillator generating continuous network, there are two methods of implementing a NTT Technical Review Vol. 17 No. 12 Dec. 2019 9 Feature Articles Brain Quantum (Critical phenomena (Quantum-classical in neural networks) crossover) Optics (Optical parametric Focus on the interdisciplinary field oscillators) of quantum, brain, and optics Fig. 1. Research fields at Physics & Informatics Laboratories (PHI Labs). Pump optical Signal optical pulses Pump optical Signal optical pulses LO pulses pulses pulses SHG pulse #2 #2 #1 #1 SHG SHG Homodyne Optical parametric Optical parametric detection amplifier PSA amplifier Optic fiber Output coupler Optic fiber ring resonator ring resonator Targeted Targeted MOD1 MOD2 … MODN–1 optical pulse optical #pulsei #i ADC FPGA Feedback optical pulse DAC Feedback optical pulse IM/PM (a) Optical delay line coupling (b) Measurement feedback coupling ADC: analog-to-digital converter LO: local oscillator DAC: digital-to-analog converter MOD: optical modulator FPGA: field-programmable gate array PSA: phase sensitive amplifier IM/PM: intensity modulation/phase modulation SHG: second harmonic generation Fig. 2. Neural network configuration based on optical parametric oscillators. fully connected neural network in which synapse [Jij] through (N–1) optical delay lines and the same connections are formed between all neurons (Fig. 2). number of optical modulators [4]. With this method, These methods use N optical parametric oscillator (N–1) input pulses j simultaneously couple with a pulses circulating in an optical fiber ring cavity of 1 single target pulse i at each time point via coupling to 10 km for N neurons instead of using N optical coefficient Jij, so N (N–1) Jij coefficients are imple- parametric oscillators, a scheme that achieves N mented for each round trip to achieve the above for all defect-free uniform neurons simultaneously within a N target pulses. This method has the advantage of single cavity [4–6]. simplifying the implementation of synapse coupling The optical delay line coupling method (Fig. 2(a)) having directionality (Jij ≠ Jji). can achieve N (N–1) synapse coupling coefficients The measurement feedback coupling method NTT Technical Review Vol. 17 No. 12 Dec. 2019 10 Feature Articles (Fig. 2(b)), on the other hand, can achieve N (N–1) diagnosis (community detection) and portfolio opti- all-synapse coupling with just a single measurement mization in the Fintech field. feedback circuit [5, 6]. The former method is thought Still another type of problem representative of com- to be applicable to the implementation of large-scale, binatorial optimization problems is the satisfiability high-speed, and sparsely coupled neural networks (SAT) problem. A coherent SAT solver that can solve and to quantum many-body problems. The latter this problem with good efficiency can be achieved by method, however, is thought to be applicable to the configuring a recurrent neural network with degener- implementation of medium-scale, high-order nonlin- ate optical parametric oscillators [10]. One specific ear coupling and densely coupled neural networks type of problem that could be solved by a coherent and to combinatorial optimization problems. SAT solver is hardware/software verification. The concept of quantum-inspired optimization has 2. Application fields recently been attracting attention as a practical solver targeting combinatorial optimization problems. This section introduces the application fields envi- Instead of actually constructing an optical (or super- sioned for quantum neural networks using optical conducting) parametric oscillator network, we apply parametric oscillators. this concept, which is aimed at obtaining optimal solutions by programming the quantum mechanical 2.1 Combinatorial optimization problems equations of motion that describe the experimental The Ising model is highly representative of combi- quantum neural network as an algorithm in a standard natorial optimization problems. This model can be digital circuit such as a field-programmable gate implemented through the use of degenerate optical array and conducting a type of numerical simulation parametric oscillators in which the signal wave and [8, 11]. idler wave have identical frequencies [3]. As a result of recent improvements in hardware technology for 2.2 Quantum many-body problems achieving a degenerate optical parametric oscillator The development of new tools for achieving effi- network together with the advancement in associated cient numerical simulations with good accuracy of algorithms, the performance of the coherent Ising electron behavior within a solid, especially of corre- machine, a type of quantum neural network, is mak- lated electron systems having strong interactions ing significant gains. In fact, it is becoming superior among electrons, is essential to searching for new to the quantum annealing machine—a type of quan- materials (material informatics) and discovering new tum computer specialized for combinatorial optimi- phenomena (topological physics). In particular, two- zation problems—and von Neumann computers dimensional systems in which electrons are confined implementing advanced algorithms such as Breakout by two-dimensional potential forces exhibit novel Local Search [7, 8]. Expectations are high that the era quantum phenomena not found in ordinary three- of solving a variety of combinatorial optimization dimensional systems. However, unlike three-dimen- problems will eventually arrive by mapping them to sional systems, numerical simulations based on the Ising model to achieve a general-purpose optimi- mean-field approximation tend to break down in two- zation solver. Application algorithms are now being dimensional systems, and it is also difficult to obtain developed for specific problems such as lead optimi- exact solutions in two-dimensional systems as in one- zation in drug discovery and the development of dimensional systems. optimum biocatalysts, resource allocation in wireless This state of affairs