基於原始閘用來刻劃量子閘保真度的隨機標竿分析法

Abstract

隨著越來越多的量子位元能使用，量子邏輯閘的錯誤率變成急迫的議題。現今有許多刻劃量子邏輯閘保真度的協議，像是量子過程解析。然而，因為量子過程解析需要的資源成指數成長隨著量子位元數目變大，所以量子過程解析不在適用。此外，量子過程解析無法區分態準備錯誤與測量錯誤與量子閘錯誤。隨機標竿分析法能夠區分態準備錯誤與測量錯誤與量子閘錯誤且所需的資源少於量子過程解析。現今，隨機標竿分析法比起量子過程解析被更頻繁的使用。然而，隨機標竿分析法在實驗中有些不同於理論中的要求。也就是說，理論上的隨機標竿分析法假設在實際實驗中是不實際的。我們在這篇論文中分析理論以及實驗的隨機標竿分析法差別且介紹新的方法叫做基於原始閘的隨機標竿分析法。我們的基於原始閘的隨機標竿分析法能夠更貼近實驗上的結果。透過數值模擬，我們展現我們的基於原始閘的隨機標竿分析法比起理論隨機標竿分析法以及實驗隨機標竿分析法有更多優勢。

Recently with more and more qubits becoming available and functional, the errors on qubit operations become an urgent issue. There are many protocols for characterizing quantum gate operations such as quantum process tomography (QPT). However, when the number of qubits become larger, QPT is no longer appropriate due to its required resources exponentially growing with qubit size. In addition, QPT mixes the state preparation and measurement (SPAM) errors with the gate errors. Instead, randomized benchmarking (RB), another method for estimating the gate error rate, can separate the SPAM errors from the gate errors. Moreover, the resource requirement by RB is less than that by QPT. Nowadays, RB are frequently used to characterize quantum gate operations. However, the situations to perform RB in experiments is a little bit different from the RB theory requirements. That is, the assumptions in some RB theory are impractical in the real experiments. We will analyse the discrepancies and introduce our new method based RB, called primitive randomized benchmarking (PRB). Our new method, PRB, can be made closer to the real RB experiments. Through numerical simulations, we show that our proposed PRB has several appealing advantages over RB and RB with decomposition into primitive gates.