Nonstoquastic Hamiltonians and quantum annealing of an Ising spin glass
Name
PhysRevB.95.184416.pdf
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Author(s)
Hormozi, Layla
Brown, Ethan W.
Carleo, Giuseppe
Troyer, Matthias
Date Issued
May 2017
Journal
Physical Review B
Publisher
American Physical Society
Citation
Hormozi, Layla et al. “Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass.” Physical Review B 95.18 (2017): n. pag. © 2017 American Physical Society
Version
Final published version
Abstract
We study the role of Hamiltonian complexity in the performance of quantum annealers. We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and nonstoquastic ones, which cannot be treated efficiently. We implement the latter by adding antiferromagnetically coupled two-spin driver terms to the traditionally studied transverse-field Ising model, and compare their performance to that of similar stoquastic Hamiltonians with ferromagnetically coupled additional terms. We focus on a model of long-range Ising spin glass as our problem Hamiltonian and carry out the comparison between the annealers by numerically calculating their success probabilities in solving random instances of the problem Hamiltonian in systems of up to 17 spins. We find that, for a small percentage of mostly harder instances, nonstoquastic Hamiltonians greatly outperform their stoquastic counterparts and their superiority persists as the system size grows. We conjecture that the observed improved performance is closely related to the frustrated nature of nonstoquastic Hamiltonians.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.95.184416
