Active suppression of dephasing in Josephson-junction qubits

TL;DR

This paper investigates a simple majority code for correcting multiple dephasing errors in Josephson-junction qubits, deriving equations for the evolution of encoded quantum information under correlated noise, and proposing a specific circuit design.

Contribution

It introduces a quantitative analysis of a majority code for dephasing error correction and suggests a Josephson-junction circuit implementation.

Findings

Derived an equation for the evolution of encoded quantum information under dephasing noise.

Proposed a specific Josephson-junction circuit design for implementing the error correction scheme.

Analyzed the effectiveness of the code in correcting multiple dephasing errors.

Abstract

Simple majority code correcting $k$ dephasing errors by encoding a qubit of information into $2k+1$ physical qubits is studied quantitatively. We derive an equation for quasicontinuous evolution of the density matrix of encoded quantum information under the error correction procedure in the presence of dephasing noise that in general can be correlated at different qubits. Specific design of the Josephson-junction circuit implementing this scheme is suggested.