GeneCS: Synthesizing Resource-Efficient Code Surgery for Arbitrary Quantum Stabilizer Codes

TL;DR

GeneCS is a compiler that significantly reduces resource overhead for quantum stabilizer code operations, enabling practical fault-tolerant quantum computing with large codes.

Contribution

It introduces a structure-aware, resource-efficient compiler for code surgery protocols applicable to arbitrary stabilizer codes, reducing ancilla requirements substantially.

Findings

Achieves over 85% reduction in ancillary qubits and checks.

Scales to codes with over 10,000 qubits with about one second per compilation.

Preserves logical error rates while optimizing resource usage.

Abstract

Efficiently realizing logical operations on general stabilizer codes remains a long-standing challenge in fault tolerant quantum computing. While code surgery provides a general framework with provable guarantees by joint logical measurements, existing constructions are largely theoretical and incur substantial ancilla overhead in practice. In this work, we propose GeneCS, a resource-efficient compiler for synthesizing code surgery protocols for arbitrary stabilizer codes. Our approach leverages structure-aware optimizations to eliminate redundancy in graph construction, dynamically balance expansion and congestion, and incorporate code degree constraints. Experimental results show that GeneCS achieves an average reduction of over $85\%$ in ancillary qubits and checks for both single-code and cross-code logical operations, while preserving logical error rates. Moreover, our compiler scales to codes with more than $10^4$ qubits with an amortized compilation time of about one second per instance. These results enable practical logical operations and efficient cross-code communication, thereby supporting the deployment of modern QLDPC codes and heterogeneous quantum architectures.