Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer (1805.05217v3)

Abstract: 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.

• The paper demonstrates that coherent Ising machines (CIMs) significantly outperform D-Wave quantum annealers on dense NP-hard problem instances.
• The study shows that CIMs achieve orders-of-magnitude faster time-to-solution for the SK model beyond 50 vertices due to all-to-all connectivity.
• The paper finds that D-Wave excels on sparse MAX-CUT instances, highlighting how hardware connectivity critically affects performance scaling.

Performance Analysis of Coherent Ising Machines Versus Quantum Annealing Systems

This paper examines the relative performance of two physical annealing technologies aimed at solving NP-hard optimization problems expressed through Ising models: input/output coherent Ising machines (CIMs), and the commercial quantum annealer developed by D-Wave Systems. The comparative evaluation focuses on two major NP-hard problems: the Sherrington-Kirkpatrick (SK) spin-glass model and the MAX-CUT problem, thus exploring both dense and sparse graph instances.

Key Findings and Results

1. Architectural Variations and Connectivity: The paper highlights that intrinsic connectivity plays a crucial role in the solver performance. The CIMs, which leverage all-to-all connectivity facilitated by measurement-feedback mechanisms, show superior performance on dense problem instances. In contrast, D-Wave quantum annealers, which use a Chimera architecture with limited connectivity, incur performance degradation on larger dense graphs due to embedding overhead.
2. Performance on the SK Model: The paper reports that on instances exceeding 50 vertices, CIMs outperform the D-Wave annealer significantly, highlighting several-orders-of-magnitude differences in time-to-solution. Notably, this performance advantage is chiefly attributed to CIMs' all-to-all connectivity and measurement-feedback methodology, which effectively manages problem coupling without the computational embedding overhead inherent in sparse connectivity systems like D-Wave's.
3. MAX-CUT Problem Insights: While the CIMs maintain their performance edge on dense graphs for MAX-CUT problems, D-Wave's quantum annealer excels on sparsely connected graphs, specifically on cubic graphs where it matches or minimally outperforms the CIM. This denotes the significant impact of graph sparseness on the relative performance of the two systems.
4. Scaling and Optimal Annealing Time: An evaluation of the optimal time-to-solution advocates that for both SK and MAX-CUT on dense graphs, the CIM's time scales exponentially more favorably compared to D-Wave's square-exponential scaling. Conversely, the D-Wave system displays superior scalability on the sparsest graphs.
5. Comparison to State-of-the-Art Classical Techniques: Although both systems showcase substantial potential, further advancements in coherence stabilization, connectivity extension, and error correction are necessary for them to surpass state-of-the-art classical algorithms like parallel tempering in practical optimization.

Theoretical and Practical Implications

The discrepancies in performance owing to physical connectivity underscore theoretical research directions for optimizing physical annealers through improved graph embedding techniques and enhanced connectivity architectures. The need for quantum coherence and entanglement utilization in quantum annealers directly influences long-term hardware advancements in quantum technologies.

From a practical standpoint, benchmarks such as these encourage ongoing refinement in quantum device technology. They prompt closer examination of hybrid approaches that could possibly employ both classical and quantum elements to leverage respective strengths, suggesting directions for the next generation of computation that combine both digital, quantum, and optical technologies.

Future Directions

The implications for increased connectivity in quantum annealers are clear, pressing for innovations that either lessen the embedding requirements in quantum systems or enhance their connectivity features. Simultaneously, this work incites questions about effective trade-offs in quantum advantage, fostering queries about what fundamental changes might be necessitated in device architecture to realize meaningful quantum acceleration in Ising problem computations. This comparative paper establishes a foundation from which such discussions and developments can proceed.