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.

Differential-quadrature-phase-shift quantum digital signature.

A novel quantum digital signature (QDS) scheme, called "differential quadrature phase-shift QDS," is presented. A message sender broadcasts a weak coherent pulse train with four phases of {0, π/2, π, 3π/2} and recipients create their own authentication keys from the broadcasted signal. Unlike conventional QDS protocols, there is no post-processing of information exchange between the sender and recipients and that between the recipients. Therefore, secured channels and/or authenticated channels for information exchange are not needed, and the key creation procedure is simpler than that of conventional QDS. Security issues are also discussed, using binominal distributions instead of Hoeffding's inequality utilized in conventional QDS studies, and calculation examples for system conditions achieving the QDS function are presented.

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.

Experimental demonstration of quantum digital signatures over 43 dB channel loss using differential phase shift quantum key distribution.

Ensuring the integrity and transferability of digital messages is an important challenge in modern communications. Although purely mathematical approaches exist, they usually rely on the computational complexity of certain functions, in which case there is no guarantee of long-term security. Alternatively, quantum digital signatures offer security guaranteed by the physical laws of quantum mechanics. Prior experimental demonstrations of quantum digital signatures in optical fiber have typically been limited to operation over short distances and/or operated in a laboratory environment. Here we report the experimental transmission of quantum digital signatures over channel losses of up to 42.8 ± 1.2 dB in a link comprised of 90 km of installed fiber with additional optical attenuation introduced to simulate longer distances. The channel loss of 42.8 ± 1.2 dB corresponds to an equivalent distance of 134.2 ± 3.8 km and this represents the longest effective distance and highest channel loss that quantum digital signatures have been shown to operate over to date. Our theoretical model indicates that this represents close to the maximum possible channel attenuation for this quantum digital signature protocol, defined as the loss for which the signal rate is comparable to the dark count rate of the detectors.

Experimental transmission of quantum digital signatures over 90 km of installed optical fiber using a differential phase shift quantum key distribution system.

Quantum digital signatures (QDSs) apply quantum mechanics to the problem of guaranteeing message integrity and non-repudiation with information-theoretical security, which are complementary to the confidentiality realized by quantum key distribution (QKD). Previous experimental demonstrations have been limited to transmission distances of less than 5 km of optical fiber in a laboratory setting. Here we report, to the best of our knowledge, the first demonstration of QDSs over installed optical fiber, as well as the longest transmission link reported to date. This demonstration used a 90 km long differential phase shift QKD to achieve approximately one signed bit per second, an increase in the signature generation rate of several orders of magnitude over previous optical fiber demonstrations.

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.

Quantum key distribution over a 72 dB channel loss using ultralow dark count superconducting single-photon detectors.

We report the first quantum key distribution (QKD) experiment over a 72 dB channel loss using superconducting nanowire single-photon detectors (SSPD, SNSPD) with the dark count rate (DCR) of 0.01 cps. The DCR of the SSPD, which is dominated by the blackbody radiation at room temperature, is blocked by introducing cold optical bandpass filter. We employ the differential phase shift QKD (DPS-QKD) scheme with a 1 GHz system clock rate. The quantum bit error rate (QBER) below 3% is achieved when the length of the dispersion shifted fiber (DSF) is 336 km (72 dB loss), which is low enough to generate secure keys.

Countermeasure against tailored bright illumination attack for DPS-QKD.

We propose a countermeasure against the so-called tailored bright illumination attack for differential-phase-shift QKD (DPS-QKD). By monitoring a rate of coincidence detection at a pair of superconducting nanowire single-photon detectors (SSPDs) which is connected at each of the output ports of Bob's Mach-Zehnder interferometer, Alice and Bob can detect and defeat this kind of attack. We also experimentally confirmed the feasibility of this countermeasure using our 1 GHz-clocked DPS-QKD system. In the emulation of the attack, we achieved much lower power of the bright illumination light compared with the original demonstration by using a pulse stream instead of broad pulses.

Characteristics of superconducting single photon detector in DPS-QKD system under bright illumination blinding attack.

We derive the time-dependent photo-detection probability equation of a superconducting single photon detector (SSPD) to study the responsive property for a pulse train at high repetition rate. Using this equation, we analyze the characteristics of SSPDs when illuminated by bright pulses in blinding attack on a quantum key distribution (QKD). We obtain good agreement between expected values based on our equation and actual experimental values. Such a time-dependent probability analysis contributes to security analysis.

Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers.

A high speed physical random bit generator is applied for the first time to a gigahertz clocked quantum key distribution system. Random phase-modulation in a differential-phase-shift quantum key distribution (DPS-QKD) system is performed using a 1-Gbps random bit signal which is generated by a physical random bit generator with chaotic semiconductor lasers. Stable operation is demonstrated for over one hour, and sifted keys are successfully generated at a rate of 9.0 kbps with a quantum bit error rate of 3.2% after 25-km fiber transmission.

Polarization-independent, differential-phase-shift, quantum-key distribution system using upconversion detectors.

We propose and demonstrate a polarization-independent, differential-phase-shift, quantum-key distribution system with upconversion detectors. Even though the detectors have polarization dependency, use of alternative polarization modulation and a two-bit delay interferometer achieves polarization-insensitive operation. In an experiment, sifted key bits were polarization-independently generated over 50 km fiber.

Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs.

We report what we believe to be the first differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs. We employed two outstanding techniques. As an entangled photon source, we used a 1.5 microm band entangled photon pair source based on spontaneous four-wave mixing in a cooled dispersion-shifted fiber. As receivers, photon pairs were actively phase modulated with LiNbO3 phase modulators followed by very stable planar light-wave circuit Mach-Zehnder interferometers, which provided two nonorthogonal measurements. As a consequence, we successfully generated sifted keys with a quantum bit error rate of 8.3% and a key generation rate of 0.3 bit/s and revealed the feasibility of this QKD scheme.

Differential-phase-shift quantum key distribution with an extended degree of freedom.

Differential-phase-shift quantum key distribution (DPS-QKD) with an extended degree of freedom of measurement is proposed. Extending the degree of freedom makes it possible to strengthen the DPS-QKD scheme against intercept-and-resend attacks. The feasibility of this idea is experimentally demonstrated.