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Domain wall encoding of discrete variables for quantum annealing and QAOA

Chancellor, Nicholas

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In this paper I propose a new method of encoding discrete variables into Ising model qubits for quantum optimization. The new method is based on the physics of domain walls in one dimensional Ising spin chains. I find that these encodings and the encoding of arbitrary two variable interactions is possible with only two body Ising terms. Following on from similar results for the `one hot' method of encoding discrete variables [Hadfield et. al. Algorithms 12.2 (2019): 34] I also demonstrate that it is possible to construct two body mixer terms which do not leave the logical subspace, an important consideration for optimising using the quantum alternating operator ansatz (QAOA). I additionally discuss how, since the couplings in the domain wall encoding only need to be ferromagnetic and therefore could in principle be much stronger than anti-ferromagnetic couplers, application specific quantum annealers for discrete problems based on this construction may be beneficial. Finally, I compare embedding for synthetic scheduling and colouring problems with the domain wall and one hot encodings on two graphs which are relevant for quantum annealing, the chimera graph and the Pegasus graph. For every case I examine I find a similar or better performance from the domain wall encoding as compared to one hot, but this advantage is highly dependent on the structure of the problem. For encoding some problems, I find an advantage similar to the one found by embedding in a Pegasus graph compared to embedding in a chimera graph.


Chancellor, N. (2019). Domain wall encoding of discrete variables for quantum annealing and QAOA. Quantum Science and Technology, 4(4), Article 045004.

Journal Article Type Article
Acceptance Date Jul 19, 2019
Online Publication Date Aug 6, 2019
Publication Date Oct 31, 2019
Deposit Date Aug 2, 2019
Publicly Available Date Aug 6, 2019
Journal Quantum Science and Technology
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 4
Issue 4
Article Number 045004


Published Journal Article (1.2 Mb)

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Copyright Statement
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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