AI 中文总结
本文提出量子电路架构见证的通用框架，通过半定规划构建见证以证明幺正变换与电路架构不兼容，针对Clifford幺正变换可简化为线性规划，实现高效数值与解析证明，可用于量子电路优化编译及设备基准测试。
AI 中文摘要
确定目标幺正变换能否在规定的量子电路架构内实现，是量子信息领域的基础问题，对量子电路的优化与编译、硬件高效量子计算具有直接影响。现有综合与编译方法主要是构造性的，但通常无法提供严格的证明，证明某幺正变换无法利用给定的实现资源完成。本文引入一种通用框架以定义量子电路架构见证，该见证可证明某幺正变换与指定量子电路架构不兼容。我们将见证的构建表述为半定规划问题，通过最大化目标幺正变换的Choi态与被测电路的Choi态之间的保真度来实现。所得见证提供了实用且量化的不兼容证明，暗示了门数或电路深度等实现资源的下界，还可在实验中用于量子设备的基准测试，证明所实现的幺正信道超出了给定电路架构的能力范围。对于Clifford幺正变换，我们利用稳定子形式体系将构建简化为线性规划，既能对包含约7个两量子比特门的电路实现更高效的数值证明，也能对由任意数量门组成的某些架构族提供解析见证。
英文摘要
Determining whether a target unitary can be implemented within a prescribed quantum circuit architecture is a fundamental problem in quantum information, with direct implications for optimisation and compilation of quantum circuits, and hardware-efficient quantum computation. While existing synthesis and compilation methods are primarily constructive, they generally do not provide rigorous certificates that a unitary cannot be realised using given implementation resources. Here we introduce a general framework to define quantum circuit architecture witnesses, which certify the incompatibility of a unitary transformation with a specified quantum circuit architecture. We formulate the witness construction as a semidefinite program by maximising the fidelity between the Choi state of the target unitary and those of tested circuits. The resulting witnesses provide practical and quantitative certificates of incompatibility, implying lower bounds on implementation resources such as the gate count or circuit depth, and can also be used experimentally to benchmark quantum devices by certifying that an implemented unitary channel goes beyond the capabilities of a given circuit architecture. For Clifford unitaries, we exploit the stabiliser formalism to reduce the construction to linear programming, enabling both more efficient numerical certification for circuits containing on the order of seven two-qubit gates, and analytical witnesses for some families of architectures made of an arbitrary number of gates.
Comments7 pages + 10 pages of appendices, 5 + 5 figures
