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arXiv · 2608.00189

Phase transitions in quantum-circuit compilation

Andrea De Girolamo·Davide Rattacaso·Simone Notarnicola·Ilaria Siloi·Simone Montangero
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Abstract

Quantum-circuit compilation aims at finding an optimized realization of a target circuit under given constraints, e.g., the minimization of hardware-induced errors and the unitary-equivalence of the circuit. We connect the compilation process with the thermodynamics of a many-body spin system: circuit infidelity plays the role of the energy function and low-temperature states correspond to compiled circuits. In the paradigmatic case where crosstalk between parallel gates is present, we find a phase transition between a disordered phase and an antiferromagnetic brick-wall phase, compatible with the Ising universality class. At larger crosstalk, we observe a $\mathbb{Z}_3$-ordered regime, suggesting that increasingly serial compiled circuits are associated with emergent $\mathbb{Z}_n$-ordered phases. When the unitary-equivalence constraint is removed, these phases disappear, showing that the equivalence between circuits underlies the emergent criticality and constitutes a source of complexity in quantum-circuit compilation and, more generally, in equivalence-constrained optimization. Finally, we observe that the Kolmogorov complexity of the circuit enhances the emergence of ordered phases.

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Andrea De Girolamo, Davide Rattacaso, Simone Notarnicola, Ilaria Siloi, Simone Montangero. 2026-07-31. Phase transitions in quantum-circuit compilation. https://arxiv.org/abs/2608.00189

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