Single-shot preparation of hypergraph product codes via dimension jump

TL;DR

This paper introduces a fault-tolerant, single-shot method for preparing hypergraph product codes in constant depth, significantly improving initialization efficiency for quantum error correction.

Contribution

The authors develop a novel protocol for constant-depth, single-shot preparation of hypergraph product codes that is robust against measurement errors, inspired by topological code techniques.

Findings

Preparation depth is constant, independent of code size.

Protocol maintains robustness despite measurement errors.

Spatial overhead is optimized to O(√n).

Abstract

Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(\sqrt{n})$ spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures.