Improving success probability in Lechner-Hauke-Zoller parity embedding by computing with quantum walks

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Bennett, Jemma and Chancellor, Nicholas and Kendon, Viv and Lechner, Wolfgang (2025) Improving success probability in Lechner-Hauke-Zoller parity embedding by computing with quantum walks. Physical Review A, 112 (4). 042616. ISSN 2469-9926 (https://doi.org/10.1103/my7q-8tbj)

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Abstract

Lechner-Hauke-Zoller (LHZ) parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimization problems. Continuous-time quantum walks are a leading approach for solving quantum optimization problems. Because they populate excited states, quantum walks can avoid the exponential gap-closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation. An important question, therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on four-, five-, and six-logical-qubit Sherrington-Kirkpatrick Ising spin glass instances embedded onto the LHZ parity embedding, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we identified postreadout error correction techniques which improve the success probability of the quantum walk.

ORCID iDs

Bennett, Jemma, Chancellor, Nicholas, Kendon, Viv ORCID logoORCID: https://orcid.org/0000-0002-6551-3056 and Lechner, Wolfgang;
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