Perfect quantum error correction coding in 24 laser pulses

TL;DR

This paper presents an optimized quantum error correction circuit for a single qubit, implemented with 24 laser pulses, and compares different error correction schemes including the quantum Zeno effect.

Contribution

It introduces a more efficient 24-pulse quantum error correction circuit for single qubits and compares its performance with other schemes.

Findings

The 24-pulse circuit effectively corrects arbitrary 1-qubit errors.

Quantum Zeno error correction fails under phase-diffusion noise.

The new circuit improves efficiency over previous implementations.

Abstract

An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum Zeno effect and the other using standard methods, is compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase-diffusion.