A Unitary Encoder for Surface Codes

TL;DR

This paper introduces a non-local unitary circuit for surface code encoding that reduces gate count and improves efficiency, with numerical evidence showing advantages over previous methods in certain quantum hardware settings.

Contribution

A novel non-local unitary encoder for surface codes based on code conversion, halving the gate count and enabling efficient state preparation in non-local quantum platforms.

Findings

Halves the gate count compared to previous encoders

Effective in preparing eigenstates under realistic noise

Compatible with non-local quantum hardware platforms

Abstract

The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a code conversion between rotated and regular surface codes, which halves the gate count of the fastest encoder known previously. While the unitary encoders can be used to increase the code distance, the fault-distance remains fixed. Nonetheless, they can be used for space-time efficient realization of eigenstates of the surface code operators that can't be easily accessed transversally such as the Pauli Y-eignestate and Clifford eigenstates. It may be expected that error propagation in the non-local circuit will make decoding more challenging compared to local unitary encoding circuits. However, we find this not to be the case and that conventional matching decoders can be effectively used. Furthermore, we perform numerical simulations to benchmark the performance of our encoder against a previous local unitary encoder and the conventional stabilizer-measurement based encoder for preparing the Pauli Y-eigenstate and find that our encoder can outperform these in experimentally relevant noise regimes. Therefore, our encoder provides practical advantage in platforms where non-local interactions are available such as neutral atoms and trapped ions.