Synthesis of Fault-tolerant State Preparation Circuits using Steane-type Error Detection

TL;DR

This paper introduces an automated method for designing fault-tolerant state preparation circuits for quantum error correction that works with any CSS code, reducing overhead and enabling practical quantum computing.

Contribution

It presents a general synthesis approach for fault-tolerant state preparation circuits applicable to all CSS codes, independent of code symmetries.

Findings

Successfully synthesized circuits for CSS codes up to distance 7.

Demonstrated fault-tolerant initialization under circuit-level depolarizing noise.

Provides a pathway for experimental realization of high-fidelity ancilla states.

Abstract

Fault-tolerant state preparation is essential for reliable quantum error correction, particularly in Steane-type error correction, which relies on robust ancilla states for syndrome readout. One method of fault-tolerant state preparation is to initialize multiple ancilla states and check them against each other to detect problematic errors. In the worst case, the number of states required for successful initialization grows polynomially with the code distance, but it has been shown that this can be reduced to constant ancilla overhead-in the best case, only four states are required. However, existing techniques for finding low-overhead initialization schemes are limited to codes with large symmetry groups, such as the Golay code. In this work, we propose a general, automated synthesis methodology for Steane-type fault-tolerant state preparation circuits that applies to arbitrary Calderbank-Shor-Steane (CSS) codes and does not rely on code symmetries. We apply the proposed methods to various CSS codes up to a distance of seven and simulate the successful fault-tolerant initialization of logical basis states under circuit-level depolarizing noise. The circuits synthesized using the proposed methodology provide an important step towards experimental realizations of high-fidelity ancilla states for near-term demonstration of fault-tolerant quantum computation.