Fault-tolerant quantum computation

Abstract

This work analyzes fault-tolerance in quantum computation, namely the use of quantum error correction to prevent the propagation and multiplication of errors in a quantum circuit. A simple quantum circuit for Bell-state preparation is studied and considered in order to theoretically determine the threshold probability pth using Steane code. This threshold corresponds to the maximum admissible error probability for each physical component gate of the circuit. Two error-correction schemes are compared: one applying a single correction at the end of the circuit, another implementing intermediate corrections. In both cases, a threshold of the order of pth ∼ 10−4 is obtained, corresponding to a fidelity of 99,99% per gate. But only the second scheme is suitable for large circuits. The theoretical threshold is compared with recent experimental results, demonstrating the practical feasibility of fault-tolerant quantum computation.