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

TL;DR

This paper analytically evaluates the fidelity of a three-qubit phase-flip error correction code implemented with superconducting qubits, considering realistic interactions and error rates, demonstrating its practical feasibility with current technology.

Contribution

Provides analytical fidelity expressions for a three-qubit phase-flip code in superconducting systems, considering specific interaction schemes and error conditions, showing practical implementation feasibility.

Findings

The code improves fidelity even at high error probabilities.

Maximum operation times for effective error correction are within current technological capabilities.

Two interaction schemes, $\sigma_z \sigma_z$ and cavity-mediated, are analyzed for implementation.

Abstract

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 dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one $\sigma_z\sigma_z$-coupling and one cavity mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology.