Quantum Annealing amid Local Ruggedness and Global Frustration (1701.04579v2)

Abstract: A recent Google study [Phys. Rev. X, 6:031015 (2016)] compared a D-Wave 2X quantum processing unit (QPU) to two classical Monte Carlo algorithms: simulated annealing (SA) and quantum Monte Carlo (QMC). The study showed the D-Wave 2X to be up to 100 million times faster than the classical algorithms. The Google inputs are designed to demonstrate the value of collective multiqubit tunneling, a resource available to D-Wave QPUs but not to simulated annealing. But the computational hardness in these inputs is highly localized in gadgets, with only a small amount of complexity coming from global interactions, meaning that the relevance to real-world problems is limited. In this study we provide a new synthetic problem class that addresses the limitations of the Google inputs while retaining their strengths. We use simple clusters instead of more complex gadgets and more emphasis is placed on creating computational hardness through frustrated global interactions like those seen in interesting real-world inputs. The logical problems used to generate these inputs can be solved in polynomial time [J. Phys. A, 15:10 (1982)]. However, for general heuristic algorithms that are unaware of the planted problem class, the frustration creates meaningful difficulty in a controlled environment ideal for study. We use these inputs to evaluate the new 2000-qubit D-Wave QPU. We include the HFS algorithm---the best performer in a broader analysis of Google inputs---and we include state-of-the-art GPU implementations of SA and QMC. The D-Wave QPU solidly outperforms the software solvers: when we consider pure annealing time (computation time), the D-Wave QPU reaches ground states up to 2600 times faster than the competition. In the task of zero-temperature Boltzmann sampling from challenging multimodal inputs, the D-Wave QPU holds a similar advantage as quantum sampling bias does not seem significant.

Quantum Annealing amid Local Ruggedness and Global Frustration: A Critical Analysis

The paper "Quantum Annealing amid Local Ruggedness and Global Frustration" by King et al. contributes significantly to the ongoing evaluation of quantum processing units (QPUs) developed by D-Wave Systems, with a focus on performance in synthetic problem classes. The paper explores the effectiveness of the 2000-qubit D-Wave QPU in solving complex optimization problems with specific interest in problem characteristics such as local ruggedness and global frustration. The research highlights two main contributions: the introduction of a new class of synthetic problems, named Frustrated Cluster Loop (FCL) problems, and the application of these to measure the D-Wave QPU’s capabilities.

New Problem Class for Evaluation

The FCL problems are intricately designed to evaluate quantum annealers under conditions that mimic real-world problems more closely than previously used problem classes, such as the Google problems. This is achieved by constructing Ising model instances with planar spin-glass backbones that incorporate significant frustration and computational hardness. Specifically, FCL problems use simple clusters for local ruggedness and intertwine global frustration through logical interactions, an approach that better represents practical optimization challenges. Notably, the input generation allows for a tunable ruggedness parameter, offering a controlled environment for assessing both classical and quantum optimization algorithms.

Performance Evaluation against Classical Solvers

In assessing the performance of the 2000-qubit D-Wave QPU, the paper juxtaposes its capability against state-of-the-art classical solvers, including simulated annealing (SA), quantum Monte Carlo (QMC), spin vector Monte Carlo (SVMC), and a tailored Hamze-de Freitas-Selby (HFS) algorithm. The results indicate that the D-Wave QPU demonstrates a significant computational speed advantage, achieving up to 2600 times faster solution times compared to the classical solvers, particularly when ruggedness increases. This advantage is showcased across several metrics, including expected time to solution (TTS) and zero-temperature Boltzmann sampling accuracies.

Insights into Quantum Annealing Dynamics

The paper adeptly discusses the implications of quantum dynamics, comparing them with classical and heuristic approaches in handling rugged energy landscapes. It highlights that QMC simulations approach the dynamics of quantum annealing more accurately than SA, supporting the hypothesis that quantum annealers leverage tunneling to navigate complex energy terrains effectively. Furthermore, the maintained performance of the D-Wave QPU in multimodal input samples suggests robustness against quantum sampling bias—a common concern in practical applications.

Future Prospects and Theoretical Implications

King et al.'s research provides valuable insights into the scaling behavior and robustness of quantum annealers, pointing towards the potential for broader applications in both real-world optimization tasks and theoretical explorations. The successful implementation of ruggedness as a tunable parameter indicates promising future research directions where quantum processors may outperform classical counterparts in more diverse problem domains.

In sum, the work presents a thorough and methodically rigorous analysis of D-Wave's latest QPU. It reinforces the potential applicability of quantum annealing in complex optimization scenarios and lays a path for further advancements in quantum computing technologies. The advent of denser, more fault-tolerant quantum processors may only expand the frontier of solvable problems, facilitating more nuanced comparisons with classical computational strategies.