Quantum versus Classical Annealing of Ising Spin Glasses (1411.5693v1)

Abstract: The strongest evidence for superiority of quantum annealing on spin glass problems has come from comparing simulated quantum annealing using quantum Monte Carlo (QMC) methods to simulated classical annealing [G. Santoro et al., Science 295, 2427(2002)]. Motivated by experiments on programmable quantum annealing devices we revisit the question of when quantum speedup may be expected for Ising spin glass problems. We find that even though a better scaling compared to simulated classical annealing can be achieved for QMC simulations, this advantage is due to time discretization and measurements which are not possible on a physical quantum annealing device. QMC simulations in the physically relevant continuous time limit, on the other hand, do not show superiority. Our results imply that care has to be taken when using QMC simulations to assess quantum speedup potential and are consistent with recent arguments that no quantum speedup should be expected for two-dimensional spin glass problems.

Quantum versus Classical Annealing of Ising Spin Glasses

The paper, "Quantum versus Classical Annealing of Ising Spin Glasses," authored by Bettina Heim et al., critically examines the comparative efficacy of quantum annealing (QA) and classical annealing methods applied to Ising spin glass models. The investigation is particularly centered on uncovering the conditions under which quantum annealing methods might demonstrate a computational advantage or quantum speedup relative to classical methods.

Overview of Methodologies

The authors employ quantum Monte Carlo (QMC) methods to emulate quantum annealing and juxtapose these results against classical simulated annealing (SA). The central focus is the time-dependent Hamiltonian approach where QA integrates quantum tunneling to minimize energy states more effectively than classical annealing, which relies on thermal excitations.

Hamiltonians considered:

• Classical Hamiltonian $H_c$: Utilizes thermal annealing where spin variables interact under specified coupling constants $J_{ij}$ and local fields $h_i$.
• Quantum Hamiltonian $H_q$: Introduces a non-commuting kinetic term characterized by a transverse field, $\Gamma(t)$, which starts large and is gradually reduced.

Key Findings

1. Performance Comparison: The authors reaffirm earlier studies demonstrating a faster convergence of residual energy decay through simulated quantum annealing (SQA) in discrete-time setups, compared to simulated classical annealing (SCA). However, when continuous-time limits applicable to physical quantum devices are considered, the advantage of SQA dissipates, indicating that findings using discrete time (DT-SQA) may not translate to real-world quantum annealing scenarios.
2. Influence of Time Discretization: The paper showcases that the time discretization inherent in path-integral QMC accounts for observed advantages in DT-SQA, thus potentially misleading expectations regarding quantum speedup on physical devices.
3. Temperature Effects: Analysis demonstrates that lower temperatures facilitate crossing potential barriers in the simulated models, yielding lower residual energy conditions.
4. Practical Limitations of QA: Examination reveals that QA configurations tend to get trapped in local minima more often than SA, and results suggest QA tends to favor certain configurations based on initial conditions rather than exploring configuration space uniformly.

Implications and Future Directions

These findings inform on the limitations in using SQA as an estimator for the performance of actual quantum annealers such as those developed by D-Wave systems. The research cautions against overestimating the potential quantum speedup in two-dimensional Ising spin glasses based solely on DT-SQA results, reinforcing skepticism raised by recent studies.

It also prompts further exploration into higher-dimensional spin glasses or those exhibiting long-range coupling, where theoretical models may still unveil environments favorable for QA superiority. This enthusiasm is tempered by the need for comprehensive evaluations employing both DT and CT-SQA methodologies.

In conclusion, while quantum annealing holds promising theoretical advantages, the practical deployment and verification in real-world applications require cautious and exhaustive empirical analysis, particularly when leveraging QMC as a proxy for quantum dynamics. This paper underscores a nuanced understanding of quantum annealing potential, reminding the research community to rigorously assess the fidelity and assumptions behind each computational method employed.