Quantum codes from classical annealing

• URL: http://arxiv.org/abs/2607.19574v1
• Date: Tue, 21 Jul 2026 21:01:37 GMT
• Title: Quantum codes from classical annealing
• Abstract summary: Search for quantum error-correcting codes with high encoding rates and large distances.<n>For block lengths of up to $50$ physical qubits, our search finds state-of-the-art CSS and SWEL codes.<n>Codes found in this work are promising candidates for high-rate code demonstrations on near-term quantum computing hardware.
• Score: 0.15293427903448023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an adaptive simulated annealing algorithm to search for moderately-sized quantum error-correcting codes with high encoding rates and large distances. Our search targets two classes of stabilizer codes: (1) CSS codes, and (2) a subclass of CSS codes that we call ``self-dual with equivalent logicals'' (SWEL) codes, the latter of which which admit transversal implementations of logical Hadamard and phase gates that can be leveraged to construct fault-tolerant gate sets. The search is guided by an energy function that acts as a surrogate for the logical error rate in a code-capacity noise model, combining code distance with a count of minimum-weight logical operators to resolve the discrete plateaux that impede naïve distance optimization. For block lengths of up to $50$ physical qubits, our search finds state-of-the-art CSS and SWEL codes whose distances frequently meet or exceed the variants of the quantum Gilbert-Varshamov bound. In addition to providing favorable seed codes for fault-tolerant architectures based on code concatenation, the codes found in this work are promising candidates for high-rate code demonstrations on near-term quantum computing hardware.

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