Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction

2017/10/22 by Walter Vinci, Daniel A. Lidar
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Algorithm #Combinatorics #Computer science #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum annealing #Quantum computer #Quantum error correction #Quantum mechanics #Qubit #Reduction (mathematics) #Scalability #Scaling #Topology (electrical circuits) #quant-ph

paper · pdf · doi:10.1103/physreva.97.022308

published as Phys. Rev. A 97, 022308 (2018) · 12 pages, 5 figures

arxiv created 2017/10/22 · openalex publication_date 2018/02/06 · arxiv updated 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Nested quantum annealing correction (NQAC) is an error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree C. The nesting level C represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to 512 qubits) showed that NQAC has the potential to achieve a scalable effective-temperature reduction, T_eff\ensuremath∼C^\ensuremath-\ensuremathη, with 0<\ensuremathη\ensuremath≤2. We confirm that this scaling is preserved when NQAC is tested on a D-Wave 2000Q device (supporting up to 2048 qubits). In addition, we show that NQAC can also be used in sampling problems to lower the effective-temperature of a quantum annealer. Such effective-temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via a reduction of the effective-temperature of the quantum annealing device, our results address the problem of the ``temperature scaling law for quantum annealers,'' which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.

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