INQA Conference 2025: Jemma Bennett - University of Innsbruck

Title: Improving the success probability of LHZ using quantum walks

Abstract: The 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. Due to them populating 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 (AQC). 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 4, 5 and 6 logical qubit Sherrington-Kirkpatrick (SK) 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 post-readout error correction techniques which improve the success probability of the quantum
walk.