Simple quantum error detection and correction for superconducting qubits

TL;DR

This paper investigates simple quantum error detection and correction protocols suitable for superconducting qubits, highlighting limitations with energy relaxation and proposing practical two-qubit algorithms for current technology.

Contribution

It demonstrates that N-qubit codes are ineffective for correction under energy relaxation but useful for detection, and introduces feasible two-qubit algorithms for error management.

Findings

Repetitive N-qubit codes cannot correct energy relaxation errors.

Two-qubit codes suffice for quantum error detection in superconducting qubits.

Proposed algorithms are compatible with current phase qubit technology.

Abstract

We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N-qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into "relaxation" and "no relaxation" scenarios. Also, we propose and numerically analyze several two-qubit algorithms for quantum error detection/correction, which can be readily realized at the present-day level of the phase qubit technology.