Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation

TL;DR

This paper demonstrates that high entanglement among register qubits in one-way quantum computation can reduce gate fidelity when measurement errors occur, providing bounds to guide error management.

Contribution

It derives an inequality linking entanglement, measurement error, and gate fidelity, offering a way to estimate acceptable error levels for reliable quantum gates.

Findings

Gate fidelity decreases with increased entanglement and measurement error.

An inequality bounds the mean gate fidelity based on entanglement and error magnitude.

Guidelines for error thresholds in entangled quantum systems are provided.

Abstract

We study how entanglement among the register qubits affects the gate fidelity in the one-way quantum computation if a measurement is inaccurate. We derive an inequality which shows that the mean gate fidelity is upper bounded by a decreasing function of the magnitude of the error of the measurement and the amount of the entanglement between the measured qubit and other register qubits. The consequence of this inequality is that, for a given amount of entanglement, which is theoretically calculated once the algorithm is fixed, we can estimate from this inequality how small the magnitude of the error should be in order not to make the gate fidelity below a threshold, which is specified by a technical requirement in a particular experimental setup or by the threshold theorem of the fault-tolerant quantum computation.