Low-overhead pieceable fault-tolerant construction of logical controlled-phase circuit for degenerate quantum code

• URL: http://arxiv.org/abs/2105.07133v8
• Date: Wed, 29 Nov 2023 13:26:34 GMT
• Title: Low-overhead pieceable fault-tolerant construction of logical controlled-phase circuit for degenerate quantum code
• Authors: Chen Lin, Guowu Yang
• Abstract summary: We search for a non-transversal but fault-tolerant construction of a logical controlled-phase gate for quantum code. We find a 3-piece fault-tolerant logical CZ circuit on this code.
• Score: 11.106110829349221
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We designed an search algorithm in order to find a non-transversal but fault-tolerant construction of a logical controlled-phase gate for general [[n,1,d]] degenerate quantum code. Then we give an example to illustrate our algorithm for a quantum code called bare [[7, 1, 3]] code. This code is obtained under certain search criteria, and it possesses a simpler flag-assisted fault-tolerant syndrome measurement circuit under a standard depolarizing error model. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, such as concatenated high level elementary logical gate circuits when aim to achieve lower logical error rates, we follow our search scheme and find a 3-pieceable fault-tolerant logical CZ circuit on this code. Numerical simulations are also performed to further analyze the logical error rate of our circuit.

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