Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm and Quantum Annealing can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.

We introduce quantum utility , a new approach to evaluating quantum performance that aims to capture the user experience by considering the overhead costs associated with a quantum computation. A demonstration of quantum utility by the quantum processing unit (QPU) shows that the QPU can outperform classical solvers at some tasks of interest to practitioners, when considering the costs of computational overheads. A milestone is a test of quantum utility that is restricted to a specific subset of overhead costs and input types. We illustrate this approach with a benchmark study of a D-Wave annealing-based QPU versus seven classical solvers for a variety of problems in heuristic optimization. We consider overhead costs that arise in standalone use of the D-Wave QPU (as opposed to a hybrid computation). We define three early milestones on the path to broad-scale quantum utility. Milestone 0 is the purely quantum computation with no overhead costs and is demonstrated implicitly by positive results on other milestones. We evaluate the performance of a D-Wave Advantage QPU with respect to milestones 1 and 2: For milestone 1, the QPU outperformed all classical solvers in 99% of our tests. For milestone 2, the QPU outperformed all classical solvers in 19% of our tests, and the scenarios in which the QPU found success correspond to cases where classical solvers most frequently failed. This approach of isolating subsets of overheads for separate analysis reveals distinct mechanisms in quantum versus classical performance, which explain the observed differences in patterns of success and failure. We present evidence-based arguments that these distinctions bode well for annealing quantum processors to support demonstrations of quantum utility on ever-expanding classes of inputs and with more challenging milestones in the very near future.

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open source D-Wave Hybrid framework, uses a QPU coprocessor operating with generic parameters. Performance is evaluated for standard spin-glass problems on two lattice types with up to 11,616 spin variables, double the size that is directly programmable on any available QPU. The proposed method is shown to converge to low-energy solutions faster than an open source simulated annealing method that is either directly employed or substituted as a coprocessor in the hybrid method. Using newer Advantage QPUs in place of D-Wave 2000Q QPUs is shown to enhance convergence of the hybrid method to low energies and to achieve a lower final energy.

We define the quantum utility performance metric and three milestones, which define quantum utility as measured in some limited context. Current and previous-generation annealing quantum systems can outperform classical solvers on a variety of input classes, on Milestones 0 and 1; our tests of Milestone 2 show positive results on a small set of inputs. Characterization of the input properties that drive these outcomes suggests that future tests will yield more widespread successes on these and more challenging milestones.

This feature article surveys issues arising in the design, development, and execution of computational experiments to study algorithms. An algorithm is viewed here as an abstract model of an implemented program: experiments are performed to study the model, and new insights about the model can be applied to predict program performance. Issues related to choosing performance measures, planning experiments, developing software tools, running tests, and analyzing data are considered. Some hazards and difficulties of computational research that arise particularly in the context of algorithmic problems are also surveyed.

This is the rejoinder of the author to the commentaries and complements to her featured article “Toward an Experimental Method for Algorithm Simulation” in the same issue.

We study the asymptotic expected behavior of the First Fit and First Fit Decreasing bin packing algorithms applied to items chosen uniformly from the interval (0,u], u ≤ 1. Our results indicate that the algorithms perform even better than previously expected.