Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects

The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM

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

Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects

The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM

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

Physics Successfully Implements Lagrange Multiplier Optimization

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the principle of Least Action, the principle of Minimum Entropy Generation, and the Variational Principle. Physics also has physical annealing which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which in its quantum form is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case the machines are digital in the same sense that a flip-flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Entropy Generation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients which drive those systems actually play the role of the corresponding Lagrange Multipliers