AI 中文总结
该研究将量子电路编译与多体自旋系统热力学关联，发现存在串扰时电路编译会出现相变，移除幺正等价约束后相消失，柯尔莫哥洛夫复杂度可促进有序相涌现。
AI 中文摘要
量子电路编译旨在在给定约束下找到目标电路的优化实现，例如最小化硬件诱导误差和保证电路的幺正等价性。我们将编译过程与多体自旋系统的热力学关联起来：电路的失保真度充当能量函数，低温态对应编译后的电路。在存在并行门串扰的典型情形中，我们发现无序相与反铁磁砖墙相之间存在相变，符合伊辛普适类。在更大的串扰下，我们观测到𝟛阶有序 regime，表明愈发串行的编译电路与涌现的𝕫ₙ阶相相关联。当移除幺正等价约束时，这些相消失，说明电路间的等价性是涌现临界性的基础，也是量子电路编译乃至更广泛的等价约束优化问题中复杂性的一个来源。最后，我们发现电路的柯尔莫哥洛夫复杂度会促进有序相的涌现。
英文摘要
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.
Comments7+7 pages, 4+5 figures
