Implementation of the three-qubit phase-flip error correction code with superconducting qubits

Superconducting qubits are prone to errors due to strong interaction with their environment. A lot of work is invested in various schemes to limit these unwanted effects. One way to limit effect of errors is to perform active error correction, where the state of one qubit is encoded into several physical qubits. Here we investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of a certain type of error known as a dephasing error, but only in situations where the error rate is low.

In this work we show that the code does increase the fidelity of the encoded state even in the presence of high error probability and give analytical expressions for the fidelity. In the figure below we plot the fidelity difference between the case when error correction is performed F^min_diag, and the no coding case F^min. This is a function of t_g, the time it takes to execute the gates, and t_s, the time which the state is stored in a noisy environment. The region where coding is beneficial is indicated with the white line.

More information: L. Tornberg, M. Wallquist, G. Johansson, V.S. Shumeiko, and G. Wendin