Topology-Dependent Compilation Asymmetry in Equivariant Quantum Neural Networks: A Compile-Once-and-Relabel Solution
Year: 2026
Type: article
Abstract: Equivariant quantum neural networks are designed to preserve symmetries in quantum machine-learning data, but this property is usually verified only before hardware compilation. We show that a transpiler can preserve the expected unitary symmetry relation while compiling symmetry-related inputs into circuits with different two-qubit gate counts and physical-qubit layouts, so ideal-circuit equivariance does not guarantee symmetry at the level of compiled circuit structure. We formalise this gap with a three-level compliance hierarchy and a taxonomy separating topology-input ansätze, where the symmetry changes the gate topology the compiler sees, from parameter-input ansätze, where it changes only numerical gate parameters and provably leaves controlled-Z counts unchanged under topology-based transpilation. Auditing four published ansatz families, we observe the effect only in the topology-input case. For the Skolik permutation-equivariant weighted-graph ansatz compiled to the IBM Heron Fez simulator target at twelve qubits, sparse graph inputs produce a mean relative controlled-Z asymmetry of 7.3\% across fifty random vertex permutations, with a worst case of 22.5\%. The effect persists across all four Qiskit optimisation levels and is not removed by matched-layout compilation, implicating routing-stage sensitivity to the ordered sparse-edge gate sequence. A density sweep shows that the asymmetry is comparable across intermediate graph densities and vanishes for complete graphs, where the ansatz degenerates into the parameter-input class, and stochastic baselines attribute the realised differences to heuristic routing sensitivity rather than to differing optimal compiled costs. Finally, we propose compile-once-and-relabel, a deployment pattern that removes controlled-Z count asymmetry by construction and reduces compilation cost for orbit-based workflows.
Source: Quantum Science and Technology
Authors: Hassan Ugail, Newton Howard
Institutions: University of Bradford, Rochester Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,895
OpenAlex ID: W7223296816