10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer.

A coherent XY machine (CXYM) is a physical spin simulator that can simulate the XY model by mapping XY spins onto the continuous phases of non-degenerate optical parametric oscillators (NOPOs). Here, we demonstrated a large-scale CXYM with >47,000 spins by generating 10-GHz-clock time-multiplexed NOPO pulses via four-wave mixing in a highly nonlinear fiber inside a fiber ring cavity. By implementing a unidirectional coupling from the ith pulse to the (i + 1)th pulse with a variable 1-pulse delay planar lightwave circuit interferometer, we successfully controlled the effective temperature of a one-dimensional XY spin network within two orders of magnitude.

Continuous and long-term stabilization of degenerate optical parametric oscillators for large-scale optical hybrid computers.

The minimum requirements for an optical reservoir computer, a recent paradigm for computation using simple algorithms, are nonlinearity and internal interactions. A promising optical system satisfying these requirements is a platform based on coupled degenerate optical parametric oscillators (DOPOs) in a fiber ring cavity. We can expect advantages using DOPOs for reservoir computing with respect to scalability and reduction of excess noise; however, the continuous stabilization required for reservoir computing has not yet been demonstrated. Here, we report the continuous and long-term stabilization of an optical system by introducing periodical phase modulation patterns for DOPOs and a local oscillator. We observed that the Allan variance of the optical phase up to 100 ms was suppressed and that the homodyne measurement signal had a relative standard deviation of 1.4% over 62,500 round trips. The proposed methods represent important technical bases for realizing stable computation on large-scale optical hybrid computers.

Observation of binary phase states of time-multiplexed degenerate optical parametric oscillator pulses generated using a nonlinear fiber Sagnac loop.

We generated time-multiplexed degenerate optical parametric oscillator (DOPO) pulses using a nonlinear fiber Sagnac loop as a phase-sensitive amplifier (PSA), where the pump and amplified light in pump-signal-idler degenerate four-wave mixing can be spatially separated. By placing the PSA in a fiber cavity, we successfully generated more than 5000 time-multiplexed DOPO pulses. We confirmed the bifurcation of pulse phases to 0 or π relative to the pump phase, which makes them useful for representing Ising spins in an Ising model solver based on coherent optical oscillator networks. We also confirmed inherent randomness of the DOPO phases using the National Institute of Standards and Technology random number test.

Wideband slow short-pulse propagation in one-thousand slantingly coupled L3 photonic crystal nanocavities.

Coupled cavities have been used previously to realize on-chip low-dispersion slow-light waveguides, but the bandwidth was usually narrower than 10 nm and the total length was much shorter than 1 mm. Here we report long (0.05-2.5 mm) slow-light coupled cavity waveguides formed by using 50, 200, and 1,000 L3 photonic crystal nanocavities with an optical volume smaller than (λ/n)3, slanted from Γ-K orientation. We demonstrate experimentally the formation of a single-mode wideband coupled cavity mode with a bandwidth of up to 32nm (4THz) in telecom C-band, generated from the ultra-narrow-band (~300 MHz) fundamental mode of each L3 nanocavity, by controlling the cavity array orientation. Thanks to the ultrahigh-Q nanocavity design, coupled cavity waveguides longer than 1 mm exhibited low loss and allowed time-of-flight dispersion measurement over a bandwidth up to 22 nm by propagating a short pulse over 1,000 coupled L3 nanocavities. The highly-dense slanted array of L3 nanocavity demonstrated unprecedentedly high cavity coupling among the nanocavities. The scheme we describe provides controllable planar dispersion-managed waveguides as an alternative to W1-based waveguides on a photonic crystal chip.

10 GHz clock time-multiplexed degenerate optical parametric oscillators for a photonic Ising spin network.

A coherent Ising machine based on degenerate optical parametric oscillators (DOPOs) is drawing attention as a way to find a solution to the ground-state search problem of the Ising model. Here we report the generation of time-multiplexed DOPOs at a 10 GHz clock frequency. We successfully generated >50,000 DOPOs using dual-pump four-wave mixing in a highly nonlinear fiber that formed a 1 km cavity, and observed phase bifurcation of the DOPOs, which suggests that the DOPOs can be used as stable artificial spins. In addition, we demonstrated the generation of more than 1 million DOPOs by extending the cavity length to 21 km. We also confirmed that the binary numbers obtained from the DOPO phase-difference measurement passed the NIST random number test, which suggests that we can obtain unbiased artificial spins.

Ultimate low system dark-count rate for superconducting nanowire single-photon detector.

The dark-count rate (DCR) is a key parameter of single-photon detectors. By introducing a bulk optical band-pass filter mounted on a fiber-to-fiber optical bench cooled at 3 K and blocking down to 5 µm, we suppressed the DCR of a superconducting nanowire single-photon detector by more than three orders of magnitude. The DCR is limited by the blackbody radiation through a signal passband of 20-nm bandwidth. The figure of merit, system detection efficiency, and DCR were 2.7×10(11), 2.3%, and 10(-3) Hz, respectively. Narrowing the bandwidth to 100 GHz suppresses the DCR to 10(-4) Hz, and the figure of merit increases to 1.8×10(12).

On-chip generation and demultiplexing of quantum correlated photons using a silicon-silica monolithic photonic integration platform.

We demonstrate the generation and demultiplexing of quantum correlated photons on a monolithic photonic chip composed of silicon and silica-based waveguides. Photon pairs generated in a nonlinear silicon waveguide are successfully separated into two optical channels of an arrayed-waveguide grating fabricated on a silica-based waveguide platform.

Dispersion and light transport characteristics of large-scale photonic-crystal coupled nanocavity arrays.

We investigate the dispersion and transmission properties of slow-light coupled-resonator optical waveguides that consist of more than 100 ultrahigh-Q photonic crystal cavities. We show that experimental group-delay spectra exhibited good agreement with numerically calculated dispersions obtained with the three-dimensional plane wave expansion method. Furthermore, a statistical analysis of the transmission property indicated that fabrication fluctuations in individual cavities are less relevant than in the localized regime. These behaviors are observed for a chain of up to 400 cavities in a bandwidth of 0.44 THz.

Slow light enhanced correlated photon pair generation in photonic-crystal coupled-resonator optical waveguides.

We demonstrate the generation of quantum-correlated photon pairs from a Si photonic-crystal coupled-resonator optical waveguide. A slow-light supermode realized by the collective resonance of high-Q and small-mode-volume photonic-crystal cavities successfully enhanced the efficiency of the spontaneous four-wave mixing process. The generation rate of photon pairs was improved by two orders of magnitude compared with that of a photonic-crystal line defect waveguide without a slow-light effect.

Entanglement distribution over 300 km of fiber.

We report the distribution of time-bin entangled photon pairs over 300 km of optical fiber. We realized this by using a high-speed and high signal-to-noise ratio entanglement generation/evaluation setup that consists of periodically poled lithium niobate waveguides and superconducting single photon detectors. The observed two-photon interference fringes exhibited a visibility of 84%. We confirmed the violation of Bell's inequality by 2.9 standard deviations.

Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide.

We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.

Collective and synchronous dynamics of photonic spiking neurons.

Nonlinear dynamics of spiking neural networks have 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 optical-pump amplitude. When the photonic neurons are coupled in a network, the interaction between them 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.

A simple low-latency real-time certifiable quantum random number generator.

Quantum random numbers distinguish themselves from others by their intrinsic unpredictability arising from the principles of quantum mechanics. As such they are extremely useful in many scientific and real-world applications with considerable efforts going into their realizations. Most demonstrations focus on high asymptotic generation rates. For this goal, a large number of repeated trials are required to accumulate a significant store of certifiable randomness, resulting in a high latency between the initial request and the delivery of the requested random bits. Here we demonstrate low-latency real-time certifiable randomness generation from measurements on photonic time-bin states. For this, we develop methods to certify randomness taking into account adversarial imperfections in both the state preparation and the measurement apparatus. Every 0.12 s we generate a block of 8192 random bits which are certifiable against all quantum adversaries with an error bounded by 2-64. Our quantum random number generator is thus well suited for realizing a continuously-operating, high-security and high-speed quantum randomness beacon.

100,000-spin coherent Ising machine.

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.

Long-distance entanglement-based quantum key distribution experiment using practical detectors.

We report an entanglement-based quantum key distribution experiment that we performed over 100 km of optical fiber using a practical source and detectors. We used a silicon-based photon-pair source that generated high-purity time-bin entangled photons, and high-speed single photon detectors based on InGaAs/InP avalanche photodiodes with the sinusoidal gating technique. To calculate the secure key rate, we employed a security proof that validated the use of practical detectors. As a result, we confirmed the successful generation of sifted keys over 100 km of optical fiber with a key rate of 4.8 bit/s and an error rate of 9.1%, with which we can distill secure keys with a key rate of 0.15 bit/s.

Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO(3) waveguide.

Entangled photon pairs are one of the most important resources for the development of quantum communication technologies. In order to produce pulsed photon pairs in the telecommunication band from 1.5 mum pump light, most of the previous experiments used two successive periodically poled lithium niobate (PPLN) waveguides. We report what we believe to be a new method using cascaded second-order nonlinearity in a single PPLN waveguide to produce high-purity time-bin entangled photon pairs. We confirmed the generation of entanglement through a two-photon interference experiment showing a coincidence fringe with a visibility of up to 97%.

Entanglement generation using silicon photonic wire waveguide.

This paper reviews recent progress on telecom-band entangled photon-pair sources based on spontaneous four-wave mixing (SFWM) in a silicon photonic wire waveguide. Thanks to the large third order nonlinearity of nano-scale silicon waveguides, we can generate photon pairs efficiently. Moreover, the use of silicon waveguides enable us to avoid the noise photons caused by spontaneous Raman scattering, which has been a serious problem with entanglement sources based on SFWM in dispersion shifted fiber. We successfully demonstrated high-purity time-bin and polarization entanglement generation using 1-cm long silicon waveguides.

Entanglement swapping using telecom-band photons generated in fibers.

We report the first entanglement swapping experiment using entangled photon-pair sources based on spontaneous four-wave mixing (SFWM). The 1.5-microm band entangled photon pairs generated by SFWM in two independent 500-m dispersion shifted fibers exhibited quantum interference, thanks to the negligible walk-off between the pump and photon pairs. The use of 500-MHz gated-mode InGaAs/InP avalanche photodiodes based on the sine-wave gating technique increased the fourfold coincidence rate. As a result, the formation of an entanglement between photons from independent sources was successfully observed.

Implementation of quantum state tomography for time-bin entangled photon pairs.

Quantum state tomography (QST) is an important method for evaluating the quality of entangled photon pairs, and has been widely used to measure polarization entanglement. However, QST has not been applied to time-bin entanglement, which is a type of entanglement suitable for fiber transmission. In this paper, we clarify the way to implement QST on time-bin entangled photon pairs using a 1-bit delayed interferometer. We also provide experimental results for a demonstration of QST for time-bin entangled photon pairs generated using spontaneous four-wave mixing in a dispersion shifted fiber.

Experimental investigation of performance differences between coherent Ising machines and a quantum annealer.

Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.