An Efficient Analytical Approach for Error Assessment in Quantum Circuits

One of the most important challenges in constructing large-scale quantum computers is handling the high error rates in quantum systems. Using error correction codes and frequently applying error correction on qubits is a common approach to compete with this challenge. Quantum error analysis techniques are required to compare the effectiveness of error correction codes and also to efficiently insert the error correction procedures (ECPs) in a quantum circuit. However, most existing assessment approaches are either inaccurate and inefficient or are slow and time-consuming. To address these problems, in this paper, a fast analytical approach is proposed that analyzes errors and smartly inserts ECPs into a quantum circuit and finally estimates the failure probability of the circuit. The approach is also able to estimate the pseudo-threshold of quantum error correction codes. Experimental results show that the proposed method improves the number of ECPs and the latency of the circuit encoded by the Steane’s [[7, 1, 3]] code on average by about 52.6% and 29.4% for the one-level one and by about 79.4% and 48.5% for the two-level concatenated code respectively compared with a related method in the literature. Moreover, the proposed method takes only a few seconds to run on even our relatively large benchmark circuits.