Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
Minh T. P. Nguyen · Mackenzie H. Shaw · 2025 · arXiv 预印本
| 编号 QCV014 | 主题 连续变量与玻色子算术 | 链接 arXiv:2511.20355 |
摘要
摘要保留原文（英文）
摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。
The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit, and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct unitary implementation of the gate using the cubic phase gate has been shown to have logical error floor unless the GKP codestate has a biased noise profile. In this work, we propose a method for on-demand noise biasing based on a standard GKP error correction circuit. This on-demand biasing circuit can be used to bias the GKP codestate before a gate and return it to a non-biased state afterwards. With the on-demand biasing circuit, we prove that the logical error rate of the gate can be made arbitrarily small as the quality of the GKP codestates increases. We complement our proof with a numerical investigation of the cubic phase gate subject to a phenomenological noise model, showing that the gate can achieve average gate fidelities above with 12 dB of GKP squeezing without the use of postselection. Moreover, we develop a formalism for finding optimal unitary representations of logical diagonal gates in higher levels of the Clifford hierarchy that is based on a framework of “polynomial phase stabilizers” whose exponents are polynomial functions of one of the quadrature operators. This formalism naturally extends to multi-qubit logical gates and even to number-phase bosonic codes, providing a powerful algebraic tool for analyzing non-Clifford gates in bosonic quantum codes.
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