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.

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.

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.

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.

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.

Understanding dynamics of coherent Ising machines through simulation of large-scale 2D Ising models.

Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines. To better understand their working principle and optimize their performance, we analyze the dynamics during the ground state search of 2D Ising models with up to 1936 mutually coupled DOPOs. For regular as well as frustrated and disordered 2D lattices, the machine finds the correct solution within just a few milliseconds. We determine that calculation performance is limited by freeze-out effects and can be improved by controlling the DOPO dynamics, which allows to optimize performance of coherent Ising machines in various tasks. Comparisons with Monte Carlo simulations reveal that coherent Ising machines behave like low temperature spin systems, thus making them suitable for optimization tasks.

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.

Four-dimensional entanglement distribution over 100 km.

High-dimensional quantum entanglement can enrich the functionality of quantum information processing. For example, it can enhance the channel capacity for linear optic superdense coding and decrease the error rate threshold of quantum key distribution. Long-distance distribution of a high-dimensional entanglement is essential for such advanced quantum communications over a communications network. Here, we show a long-distance distribution of a four-dimensional entanglement. We employ time-bin entanglement, which is suitable for a fibre transmission, and implement scalable measurements for the high-dimensional entanglement using cascaded Mach-Zehnder interferometers. We observe that a pair of time-bin entangled photons has more than 1 bit of secure information capacity over 100 km. Our work constitutes an important step towards secure and dense quantum communications in a large Hilbert space.

A coherent Ising machine for 2000-node optimization problems.

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

A fully programmable 100-spin coherent Ising machine with all-to-all connections.

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

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.

Entangled photons from on-chip slow light.

We report the first entanglement generation experiment using an on-chip slow light device. With highly efficient spontaneous four-wave mixing enhanced by the slow light effect in a coupled resonator optical waveguide based on a silicon photonic crystal, we generated 1.5-µm-band high-dimensional time-bin entangled photon pairs. We undertook two-photon interference experiments and observed the coincidence fringes with visibilities >74%. The present result enables us to realize an on-chip entanglement source with a very small footprint, which is an essential function for quantum information processing based on integrated quantum photonics.

An on-chip coupled resonator optical waveguide single-photon buffer.

Integrated quantum optical circuits are now seen as one of the most promising approaches with which to realize single-photon quantum information processing. Many of the core elements for such circuits have been realized, including sources, gates and detectors. However, a significant missing function necessary for photonic quantum information processing on-chip is a buffer, where single photons are stored for a short period of time to facilitate circuit synchronization. Here we report an on-chip single-photon buffer based on coupled resonator optical waveguides (CROW) consisting of 400 high-Q photonic crystal line-defect nanocavities. By using the CROW, a pulsed single photon is successfully buffered for 150 ps with 50-ps tunability while maintaining its non-classical properties. Furthermore, we show that our buffer preserves entanglement by storing and retrieving one photon from a time-bin entangled state. This is a significant step towards an all-optical integrated quantum information processor.

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 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.