使零階過程保真度獨立於狀態準備與測量誤差

Abstract

在這項工作中，我們證明了零保真度（過程保真度的零階）是過程保真度的近似值，可以與隨機基準測試相結合，使其對狀態準備和測量錯誤具有穩健性.然而，由於隨機基準測試需要在量子位元數量增加時在克利福德組中隨機選擇極大量的克利福德元素，因此這種組合也僅限於最多具有三個量子位元的量子系統。為了使零保真度獨立於狀態準備和測量錯誤並適用於多量子位元情況，我們採用了通道雜訊縮放方法，類似於用於量子錯誤緩解的全局酉折疊或身份縮放方法。與需要隨機選擇克利福德閘並應用最終反轉操作的隨機基準測試不同，這種恆等縮放技術插入恆等閘層（或恆等電路）以延長電路通過通道的持續時間，從而允許擬合零保真度呈指數衰減。因此，我們提出的將通道雜訊縮放與零保真度相結合的方法比用於解決量子通道零保真度中的狀態準備和測量錯誤的隨機基準測試的方法更具可擴展性和資源效率。

In this work, we demonstrated that zero-fidelity (the zeroth-order of process fidelity), an approximation to process fidelity, can be combined with randomized benchmarking to make it robust to state preparation and measurement (SPAM) errors. However, due to randomized benchmarking which requires randomly choosing an extremely large number of Clifford elements in the Clifford group when the qubit number increases, this combination is also limited to quantum systems with up to three qubits. To make the zero-fidelity independent of SPAM errors and applicable to multi-qubit cases, we employ a channel noise scaling method, similar to the method of global unitary folding or identity scaling used for quantum error mitigation. Unlike randomized benchmarking which requires choosing randomly Clifford gates and applying a final inversion operation, this technique of identity scaling inserts layers of identity gates (or identity circuits) to extend the duration of the circuit through the channel, and consequently allows fitting the zero-fidelity with exponential decay. Therefore, our proposed method of combining the channel noise scaling with the zero-fidelity is more scalable and resource-efficient than that with randomized benchmarking for addressing SPAM errors in the zero-fidelity of a quantum channel.