Quantum

Generalised Bit-Vector Abstractions for Formal Verification of Quantum Error-Detection and Entanglement Circuits over {H,X,C-NOT}: CSS Constructions, Soundness, and Mutation-Based Validation

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Briefings

This paper generalizes bit-vector abstractions for formal verification of quantum circuits, extending previous work to parametrised repetition codes and CSS constructions. The framework supports arbitrary parity-check matrices for codes like Steane and Reed-Muller, verifying up to 101 logical elements and detecting errors up to a specified weight. A mutation study using 13 operators identified 622 non-equivalent mutants, while a direct Z3 implementation verified GHZ circuits with 262,144 qubits across three topologies on a 16GB laptop. The study characterizes the {H,X,C-NOT} fragment for faithful Hilbert-space semantics, proving soundness and necessity with counterexamples.

Key points

• Formal verification of quantum circuits using bit-vector abstractions now supports parametrised repetition and concatenated phase-flip codes with up to 101 logical elements.
• Verification of syndrome extraction is possible for CSS codes specified by arbitrary parity-check matrices, including the Steane, [[15,7,3]] Hamming, [[15,1,3]] Reed-Muller, and rotated surface codes with distances up to 101.

Context and limitations

The approach does not target general stabilizer circuits, Y-type stabilizers, fault-tolerant protocols, or physical noise; extensions are needed to address these cases.

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