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

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., Warburton, P. A., & 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: Jul 19, 2022
• 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
• Public URL: https://durham-repository.worktribe.com/output/1197191