Trapped-ion quantum error-correcting protocols using only global operations

TL;DR

This paper proposes a method for quantum error correction using only global entangling operations in a trapped-ion system, significantly reducing complexity and noise during encoding and readout.

Contribution

It introduces a novel protocol for encoding and decoding quantum error-correcting codes with only global operations, enhancing efficiency and noise resilience.

Findings

Six-fold improvement in coherence time achievable

Efficient encoding and readout with minimal global pulses

Noise analysis supports high-fidelity operation at 1% noise level

Abstract

Quantum error-correcting codes are many-body entangled states that are prepared and measured using complex sequences of entangling operations. Each element of such an entangling sequence introduces noise to delicate quantum information during the encoding or reading out of the code. It is important therefore to find efficient entangling protocols to avoid the loss of information. Here we propose an experiment that uses only global entangling operations to encode an arbitrary logical qubit to either the five-qubit repetition code or the five-qubit code, with a six-ion Coulomb crystal architecture in a Penning trap. We show that the use of global operations enables us to prepare and read out these codes using only six and ten global entangling pulses, respectively. The proposed experiment also allows the acquisition of syndrome information during readout. We provide a noise analysis for the presented protocols, estimating that we can achieve a six-fold improvement in coherence time with noise as high as $\sim 1\%$ on each entangling operation.