Phase transitions in quantum-circuit compilation

• URL: http://arxiv.org/abs/2608.00189v1
• Date: Fri, 31 Jul 2026 18:14:09 GMT
• Title: Phase transitions in quantum-circuit compilation
• Abstract summary: We connect the compilation process with the thermodynamics of a many-body spin system.<n>We observe that the Kolmogorov complexity of the circuit enhances the emergence of ordered phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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