Efficient Fault-Tolerant Ancilla Preparation for Quantum BCH codes via Cyclic Symmetry

TL;DR

This paper introduces a novel, cyclic symmetry-based framework for fault-tolerant ancilla preparation in quantum BCH codes, reducing overhead and error rates for practical quantum fault-tolerance.

Contribution

It develops a low-overhead distillation method leveraging cyclic symmetry in quantum BCH codes, enabling efficient fault-tolerant ancilla preparation.

Findings

Lower spatial overhead compared to conventional circuits.

Reduced logical error rates in simulations.

Performance benchmarks under realistic noise models.

Abstract

One of the major challenges in realizing fault-tolerant quantum computers (FTQCs) is the requirement for a large number of physical qubits. To address this issue, high-rate quantum error correcting codes, which efficiently embed logical qubits into physical qubits, have recently attracted considerable attention. Among such codes, quantum BCH codes, which offer both high rates and large code distances, are promising yet underexplored candidates. However, no fault-tolerant ancilla preparation method specialized for this class had been established. We employ a two-stage approach (non-fault-tolerant preparation + entanglement distillation) for ancilla preparation. We then propose a framework for designing low-overhead distillation method that strategically leverages the cyclic symmetry of quantum BCH codes to determine which non-fault-tolerant circuits can successfully produce a fault-tolerant state. Numerical simulations on several high-performance quantum BCH codes up to 127 qubits demonstrate that our method achieves lower spatial overhead and logical error rates than conventional distillation circuits. Furthermore, we evaluated the logical error rates under a circuit-level noise model, and obtained performance benchmarks in realistic settings. This efficient state preparation technique is expected to contribute to the early realization of practical FTQCs, particularly on highly connected quantum platforms such as neutral atom systems.