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Minimizing minor embedding energy: an application in quantum annealing

Fang, Y-L; Warburton, PA; (2020) Minimizing minor embedding energy: an application in quantum annealing. Quantum Information Processing , 19 (7) , Article 191. 10.1007/s11128-020-02681-x. Green open access

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Abstract

A significant challenge in quantum annealing is to map a real-world problem onto a hardware graph of limited connectivity. When the problem graph is not a subgraph of the hardware graph, one might employ minor embedding in which each logical qubit is mapped to a tree of physical qubits. Pairwise interactions between physical qubits in the tree are set to be ferromagnetic with some coupling strength F<0. Here we address the theoretical question of what the best value F should be in order to achieve unbroken trees in the pre-quantum-processing. The sum of |F| for each logical qubit is defined as minor embedding energy, and the best value F is obtained when the minor embedding energy is minimized. We also show that our new analytical lower bound on |F| is a tighter bound than that previously derived by Choi (Quantum Inf Process 7:193–209, 2008). In contrast to Choi’s work, our new method depends more delicately on minor embedding parameters, which leads to a higher computational cost.

Type: Article
Title: Minimizing minor embedding energy: an application in quantum annealing
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11128-020-02681-x
Publisher version: http://dx.doi.org/10.1007/s11128-020-02681-x
Language: English
Additional information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: Minor embedding, Adiabatic quantum computing, Job-shop scheduling
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
URI: https://discovery.ucl.ac.uk/id/eprint/10101303
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