2018/06/07 by Masaki Ohkuwa, Hidetoshi Nishimori, Daniel A. Lidar · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Annealing (glass) #Condensed matter physics #Mathematics #Metastability #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum annealing #Quantum computer #Quantum many-body systems #Quantum mechanics #Quantum tunnelling #Qubit #Simulated annealing #Spins #Statistical physics #Superposition principle #Thermodynamics #quant-ph
paper · pdf · doi:10.1103/physreva.98.022314
published as Phys. Rev. A 98, 022314 (2018) · 22 pages, 12 figures
arxiv created 2018/06/07 · openalex created_date 2018/06/13 · openalex publication_date 2018/08/13 · arxiv updated 2018/08/21 · openalex updated_date 2026/08/05
Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic p-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the difficulty is mitigated due to a smaller jump in the order parameter at a first-order transition, which implies a larger rate of quantum tunneling. Reverse annealing has not been studied analytically before, and this study paves the way toward a systematic understanding of this relatively unexplored protocol in a broader context.