Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection

• URL: http://arxiv.org/abs/2301.12859v1
• Date: Mon, 30 Jan 2023 13:12:41 GMT
• Title: Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection
• Authors: Yuanchen Zhao, Dong E. Liu
• Abstract summary: We focus on the topological surface code, and study the case when the code suffers from both noise and coherent noise on the multi-qubit entanglement gates. We conclude that this type of unavoidable coherent errors could have a fatal impact on the error correction performance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum deviations or coherent errors are a typical type of noise encountered when implementing gate operations in quantum computers, and their impact on the performance of quantum error correction codes is still mysterious due to the lack of the analytical or numerical tools. Here we focus on the topological surface code, and study the case when the code suffers from both stochastic noise and coherent noise on the multi-qubit entanglement gates during stabilizer measurements in both initial state preparation and error detections. We map a multi-round error detection protocol to a three-dimensional statistical mechanical model consisting of Z_2 gauge interactions and related the error threshold to its phase transition point. Specifically, by analyzing the Wilson loop observables, two error thresholds are identified distinguishing different error correction performances. Above a finite error rate threshold, logical errors are unavoidable even when feeding an infinite amount of syndrome histories into the decoder. Below this threshold, there are still unidentifiable measurement errors which could also lead to the failure of error correction. This problem can only be fixed by another phase transition or error threshold residing at the perfect initial state preparation point. We conclude that this type of unavoidable coherent errors could have a fatal impact on the error correction performance.

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