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A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of the spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the obtained temperature, we confirmed that the thermodynamic quantities obtained with the CIM exhibited a phase-transition-like behavior that better matches the analytical and numerical results than the mean field one., 6 pages, 3 figures

Nonlinear dynamics of spiking neural networks has recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by collective spiking dynamics of neurons, the fine control of spiking dynamics is desirable for neuromorphic devices. Here we show that photonic spiking neurons implemented with paired nonlinear optical oscillators can be controlled to generate two modes of bio-realistic spiking dynamics by changing the optical pump amplitude. When they are coupled in a network, we found that the interaction between the photonic neurons induces an effective change in the pump amplitude depending on the order parameter that characterizes synchronization. The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems., Comment: 43 pages, 9 figures

A phase-sensitive amplifier (PSA) has the potential of low-noise optical amplification and nonlinear phase noise mitigation. For PSA operation, the chromatic dispersion (CD) that causes gain ripple must be compensated before amplification. We propose an accurate CD estimation method for non-degenerate PSAs (ND-PSAs). We experimentally demonstrated its effectiveness by using periodically poled LiNbO3 waveguides as amplification mediums. We first modified the conventional formula for the gain spectrum under residual CD conditions to be applicable to ND-PSAs by considering phase locking. We then experimentally described the effect of passband narrowing due to the gain ripple on the signal quality using a probabilistically shaped 64QAM signal. Furthermore, we applied the modified formula to CD estimation and compensation. As a result, accurate CD estimation on the sub-ps/nm order and gain-flattened spectrum over 3.5 THz were demonstrated with our method. We also propose a method for estimating residual CD from the gain variation among wavelength division multiplexing (WDM) channels. The possibility of adaptive compensation for CD was shown by carrying out WDM amplification.

Controlling the waveform of light is the key for a versatile light source in classical and quantum electronics. Although pulse shaping of classical light is a mature technique and has been used in various fields, more advanced applications would be realized by a light source that generates arbitrary quantum light with arbitrary temporal waveform. We call such a device a quantum arbitrary waveform generator (Q-AWG). The Q-AWG must be able to handle versatile quantum states of light, which are fragile. Thus, the Q-AWG requires a radically different methodology from classical pulse shaping. In this paper, we invent an architecture of Q-AWGs that can operate semi-deterministically at a repetition rate over GHz in principal. We demonstrate its core technology via generating highly non-classical states with waveforms that have never been realized before. This result would lead to powerful quantum technologies based on Q-AWGs such as practical optical quantum computing., 24 pages, 5 figures

Continuous-wave (CW) squeezed light is used in generation of various optical quantum states thus is a fundamental resource of fault-tolerant universal quantum computation using optical continuous variables. To realize a practical quantum computer, a waveguide optical parametric amplifier (OPA) is an attractive CW squeezed light source in terms of its THz-order bandwidth and suitability for modularization. The usages of a waveguide OPA in quantum applications thus far, however, are limited due to the difficulty of the generation of the squeezed light with a high purity. In this paper, we report the first observation of Wigner negativity of the states generated by a heralding method using a waveguide OPA. We generate Schr\"{o}dinger cat states at the wavelength of 1545 nm with Wigner negativity using a quasi-single-mode ZnO-doped periodically poled ${\rm LiNbO_3}$ waveguide module we developed. Wigner negativity is regarded as an important indicator of the usefulness of the quantum states as it is essential in the fault-tolerant universal quantum computation. Our result shows that our waveguide OPA can be used in wide range of quantum applications leading to a THz-clock optical quantum computer., Comment: 10 pages, 5 figures

We observed Wigner negativity of Schrödinger cat states generated with a low-loss continuous-wave optical parametric amplifier, paving the way toward fault-tolerant and universal quantum computation with terahertz clock frequency.

A configuration for wavelength conversion and optical amplification by parametric interaction using a nonlinear optical device is proposed. It enables pump generation through second harmonic generation (SHG), difference frequency generation (DFG), and optical parametric amplification (OPA) using a multiple-quasi-phase-matched (M-QPM) LiNbO3 waveguide in a bidirectional manner. Wavelength conversion for the 1.4–1.6 µm band is experimentally demonstrated. In addition, it is demonstrated that the parametric gain band can be changed using various detunings between the pump and QPM wavelengths used for the DFG/OPA process. The proposed method would be useful for enabling high-capacity optical transmission outside the 1550-nm band.

Description, We constructed a large optical computer based on optical parametric oscillators coupled via measurement and feedback., Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.

The Potts model describes Ising-model-like interacting spin systems with multivalued spin component, and ground-state search problems of the Potts model can be efficiently mapped onto various integer optimization problems thanks to the rich expression of the multivalued spins. Here, we demonstrate a solver of this model based on hybrid computation using physical and digital architectures, wherein a digital computer updates the interaction matrices in the iterative calculations of the physical Ising-model solvers. This update of interactions corresponds to learning from the Ising solutions, which allows us to save resources when embedding a problem in a physical system. We experimentally solved integer optimization problems (graph coloring and graph clustering) with this hybrid architecture in which the physical solver consisted of coupled degenerate optical parametric oscillators.

We achieved all-optical quadrature measurement of continuous-wave over-3-dB squeezed light at up to 3.7-THz sideband frequencies using LiNbO3-waveguide optical parametric amplifiers, which showed high-gain broadband phase-sensitive amplification. This technique will lead to ultrafast quantum computation.

We demonstrated a photonic spiking neuron that can represent the bio-realistic spiking modes of Class-I and Class-II neurons. In network experiments, we observed spontaneous modification of spiking mode depending on the synchronization of clustered neurons.

Phase-sensitive detection is the essential projective measurement for measurement-based continuous-variable quantum information processing. The bandwidth of conventional electrical phase-sensitive detectors is up to several gigahertz, which would limit the speed of quantum computation. It is theoretically proposed to realize terahertz-order detection bandwidth by using all-optical phase-sensitive detection with an optical parametric amplifier (OPA). However, there have been experimental obstacles to achieve large parametric gain for continuous waves, which is required for use in quantum computation. Here, we adopt a fiber-coupled $\chi^{(2)}$ OPA made of a periodically poled LiNbO${}_{3}$ waveguide with high durability for intense continuous-wave pump light. Thanks to that, we manage to detect quadrature amplitudes of broadband continuous-wave squeezed light. 3 dB of squeezing is measured up to 3 THz of sideband frequency with an optical spectrum analyzer. Furthermore, we demonstrate the phase-locking and dispersion compensation of the broadband continuous-wave squeezed light, so that the phase of the squeezed light is maintained over 1 THz. The ultra-broadband continuous-wave detection method and dispersion compensation would help to realize all-optical quantum computation with over-THz clock frequency., Comment: 7 pages, 6 figures, a typo in metadata fixed

We report a coherent Ising machine (CIM) that can simulate the Ising model with external magnetic fields. To represent Ising spins, the CIM employs degenerate optical parametric oscillator (DOPO) pulses, which are coupled by a measurement-feedback scheme. By adding to a feedback signal a term that is proportional to a given magnetic field and an absolute value of the measured amplitude of a DOPO pulse, the networked DOPO pulses behave like Ising spins in a magnetic field. Using the CIM, we implement antiferromagnetically coupled one- and two-dimensional networks of the Ising spins in uniform magnetic fields. At the field amplitudes that agree with a theoretical prediction, we experimentally observe a transition from an antiferromagnetic state governed by spin-spin interactions to a ferromagnetic state induced by the external magnetic field. In addition, staggered magnetization measurement reveals that the CIM behaves differently depending on the network dimensionality, which is consistent with the results obtained with the analytical solution and Monte Carlo simulations, but cannot be reproduced with a simple mean-field theory. These results suggest that the CIM clearly simulates the behavior of Ising spin networks better than a mere mean-field solver and will thus become a useful tool for simulating various statistical physics problems based on the Ising model.