比较和学习量子电路编译的品质因数
Comparing and learning figures of merit for quantum circuit compilation
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中文总结 AI 辅助
研究不同量子电路编译品质因数（FoM）优缺点，提出加权成功试验概率wPST，设计机器学习模型预测，在数值模拟和实验中表现优于常用FoM，并给出预测非转译电路wPST的两步法。
中文摘要 AI 辅助
为使量子算法在特定量子设备上可执行，需编译成符合硬件约束的电路，通常经多步生成多个兼容电路并选最佳，电路质量由FoM量化。常用FoM计算简单但不直接反映结构和噪声影响，复杂FoM评估耗时。本文研究不同FoM优缺点，提出wPST，设计机器学习模型预测，结果表明优于常用FoM。还给出预测非转译电路wPST的两步法。
英文摘要
To make quantum algorithms executable on a particular quantum device, they need to be compiled into circuits that respect constraints of the quantum hardware. This compilation usually involves multiple steps, where many hardware-compatible circuits are generated, and the best circuit is selected. To say which circuit is best, the quality of a circuit is generally quantified by a $\textit{figure of merit}$ (FoM). For FoMs, there is a trade-off between ease of calculation and accuracy in predicted execution quality. Commonly used FoMs, e.g., the number of gates, circuit depth, etc., are easy to evaluate, but do not directly capture the effects of circuit structure and noise. On the other end of the spectrum are FoMs that require full circuit execution and take a prohibitively long time to evaluate. One example is the probability of successful trials (PST), i.e., the probability of obtaining the initial state after running the quantum circuit followed by its inverse. Here, we investigate advantages and disadvantages of different FoMs, and formulate the properties of an ideal FoM. Based on our results, we propose wPST, a weighted version of the PST that accounts for individual qubits, not just the whole state. To quickly predict PST and wPST, we design machine learning models that take into account both the quantum circuit and quantum hardware data. In numerical simulations and experiments on quantum processors, we find that our machine learning-predicted FoMs outperform commonly used FoMs, increasing the correlation with the true PST or wPST by over 50%. To make our model useful for quantum compilers, we devise a two-step process to predict the wPST for non-transpiled quantum circuits: first, we predict the additional quantum gates required for the given quantum circuit, and then we predict the wPST, accounting for coherence times in the quantum device.
