A Universal Circuit Set Using the $S_3$ Quantum Double

• URL: http://arxiv.org/abs/2411.09697v1
• Date: Thu, 14 Nov 2024 18:58:41 GMT
• Title: A Universal Circuit Set Using the $S_3$ Quantum Double
• Authors: Liyuan Chen, Yuanjie Ren, Ruihua Fan, Arthur Jaffe,
• Abstract summary: We present a quantum double model $mathcalD(S_3)$ -- a specific non-Abelian topological code. We encode each physical degree of freedom of $mathcalD(S_3)$ into a novel, quantum, error-correcting code. Our proposal offers a promising path to realize universal topological quantum computation in the NISQ era.
• Score: 0.5231056284485742
• License:
• Abstract: One potential route toward fault-tolerant universal quantum computation is to use non-Abelian topological codes. In this work, we investigate how to achieve this goal with the quantum double model $\mathcal{D}(S_3)$ -- a specific non-Abelian topological code. By embedding each on-site Hilbert space into a qubit-qutrit pair, we give an explicit construction of the circuits for creating, moving, and locally measuring all non-trivial anyons. We also design a specialized anyon interferometer to measure the total charge remotely for well-separated anyons; this avoids fusing them together. These protocols enable the implementation of a universal gate set proposed by Cui et al. and active quantum error correction of the circuit-level noise during the computation process. To further reduce the error rate and facilitate error correction, we encode each physical degree of freedom of $\mathcal{D}(S_3)$ into a novel, quantum, error-correcting code, enabling fault-tolerant realization, at the logical level, of all gates in the anyon manipulation circuits. Our proposal offers a promising path to realize universal topological quantum computation in the NISQ era.

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