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

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

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

<症例>石灰化胃癌の1例

By upper gastrointestinal series, a 57 years-old woman was pointed out to have scattered calcifications along the greater curvature of the stomach. On computerized tomography, the calcifications distributed in the irregularly thickened gastric wall. With a diagnosis of calcified mucinous adenocarcinoma showing Borrmann type III, total gastrectomy with splenectomy was carried out. The characteristics of this lesion were briefly presented with a review of the literature.57歳女性の上部消化管透視において, 胃の大弯側に散在性の小斑点状の石灰化が指摘された. この石灰化は, 腹部コンビューター断層撮影では不規則に肥厚した胃壁内に存在した. ボールマン III 型の石灰化胃粘液腺癌の診断で胃全摘・脾摘を行った. 画像診断と肉眼標本によって石灰化を証明できた胃癌はまれであり, 本邦報告例では女性に多く, すべて進行癌であった. 腫瘍の粘液産生がこの石灰化に関与すると考えられている. また, 切除率や生存率がかなり低い疾患でもあり, 自験例も術後2年半で癌再発により死亡した. 文献的考察を加えて報告した