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 arbitrary waveform generator

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.Comment: 24 pages, 5 figure

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

Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.Comment: 12 pages, 5 figures, 1 table (main text); 14 pages, 12 figures, 2 tables (supplementary

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(–α_(DW)N^2)] relative to CIMs [exp(–α_(CIM)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

Scaling advantages of all-to-all connectivity in physical annealers: the Coherent Ising Machine vs. D-Wave 2000Q

Physical annealing systems provide a heuristic approach to solve NP-hard Ising optimization problems. It is believed that the connectivity between spins in such annealers significantly impacts the machine's computational effectiveness. In this paper we study the performance of two types of annealing machines that have very different connectivity -- a commercially available quantum annealer built by D-wave Systems, which has sparse connectivity, and coherent Ising machines based on optical parametric oscillator networks, which have all-to-all connectivity. We demonstrate an exponential (e^(−O(N^2))) penalty in performance for the D-wave quantum annealer relative to coherent Ising machines when solving Ising problems on dense graphs, which is attributable to the differences in internal connectivity between the machines. This leads to a several-orders-of-magnitude time-to-solution difference between coherent Ising machines and the D-wave system for problems with over 50 vertices. Our results provide strong experimental support to efforts to increase the connectivity of physical annealers