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Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries

Chancellor, Nicholas; Crowley, Philip J.D.; Durić, Tanja; Vinci, Walter; Amin, Mohammad H.; Green, Andrew G.; Warburton, Paul A.; Aeppli, Gabriel

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Authors

Philip J.D. Crowley

Tanja Durić

Walter Vinci

Mohammad H. Amin

Andrew G. Green

Paul A. Warburton

Gabriel Aeppli



Abstract

A finite length ferromagnetic chain with opposite spin polarization imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterizing the annealer. The noise measured in this fashion is smaller than what is seen during the single-qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

Citation

Chancellor, N., Crowley, P. J., Durić, T., Vinci, W., Amin, M. H., Green, A. G., …Aeppli, G. (2022). Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries. npj Quantum Information, 8(1), Article 73. https://doi.org/10.1038/s41534-022-00580-w

Journal Article Type Article
Acceptance Date May 20, 2022
Online Publication Date Jun 27, 2022
Publication Date 2022
Deposit Date Jul 19, 2022
Publicly Available Date Mar 29, 2024
Journal npj Quantum Information
Publisher Nature Research
Peer Reviewed Peer Reviewed
Volume 8
Issue 1
Article Number 73
DOI https://doi.org/10.1038/s41534-022-00580-w

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