What is the Computational Value of Finite Range Tunneling? (1512.02206v4)

Abstract: Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is $\sim 10^8$ times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to $\sim 10^8$ times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

• The paper investigates the computational value of finite range tunneling in quantum annealing, focusing on its potential to solve optimization problems with rugged energy landscapes more efficiently.
• The study found that for specific crafted problems with 945 variables, the D-Wave 2X quantum annealer achieved a time-to-success approximately 10^8 times faster than classical simulated annealing and quantum Monte Carlo.
• Results suggest that quantum hardware can leverage tunneling for significant speedups on certain problem types, indicating a potential scaling advantage with future improvements in quantum annealer connectivity and coherence.

Insights into the Computational Value of Finite Range Tunneling

The paper "What is the Computational Value of Finite Range Tunneling?" explores the potential advantages of using quantum annealing (QA) as a heuristic optimization method by leveraging finite range tunneling. The authors investigate the D-Wave 2X quantum annealer's performance compared to classical approaches such as Simulated Annealing (SA) and Quantum Monte Carlo (QMC). The paper is particularly focused on crafted problems with rugged energy landscapes that have tall and narrow energy barriers—the types of problems where tunneling could provide a computational advantage.

The paper's primary empirical finding is that, for instances with 945 variables, the D-Wave 2X annealer achieves a time-to-99%-success-probability that is approximately $10^8$ times faster than SA running on a single processor core. Additionally, the quantum device demonstrates a similar performance improvement over QMC, a classical algorithm mimicking quantum tunneling. These results suggest that quantum hardware can effectively utilize tunneling to navigate complex energy landscapes more efficiently than classical simulations.

In exploring the D-Wave 2X's performance, the authors crafted a specific problem domain: weak-strong cluster networks. The problem structure aims to benefit from finite range tunneling, characterized by rugged landscapes and high barriers. Within this domain, QA's success underscores finite range tunneling's role in potentially accelerating the transition across energy barriers, offering a stark advantage over purely thermal escape mechanisms such as those employed in SA.

For QA's theoretical implications, the paper notes that for single cotunneling events involving eight qubits, the performance advantage of QA over SA and QMC might grow with the problem size. This suggests that as QA hardware evolves, especially with improvements in connectivity and coherence, next-generation annealers might outperform classical solvers not only in prefactors but potentially in scaling, for problems of substantial practical interest.

From a practical perspective, while the current generation of quantum annealers is yet to demonstrate a universal quantum speedup across the board, the research provides insight into specific scenarios—characterized by rugged landscapes—where quantum annealers capitalize on tunneling to exceed classical benchmarks. The weak-strong cluster networks validate these theoretical claims within the constraints of existing hardware.

Future research directions in this domain will likely focus on developing quantum annealers with higher connectivity and reduced noise. Doing so may extend their optimization capabilities and practical applicability across a broader spectrum of nontrivial computational problems, including high-order binary optimization tasks with complex landscapes.

In summary, this work offers a compelling argument for the computational value of finite range tunneling in quantum annealing. It sheds light on situations where quantum devices may provide significant advantages over classical approaches, reinforcing the importance of advancing quantum annealing technologies and their application to broader problem classes.