Measurement-based quantum computation with variable-range interacting systems

TL;DR

This paper shows that weighted graph states generated by variable-range interacting Ising systems can implement high-fidelity quantum gates, demonstrating robustness and potential for measurement-based quantum computation.

Contribution

It introduces a method to use variable-range Ising interactions to generate resource states for MBQC with fidelities exceeding classical limits, including optimization and robustness analysis.

Findings

Fidelities of over 90% for single- and two-qubit gates above a certain fall-off rate.

Long-range interactions enable nonclassical fidelities in MBQC.

The protocol remains robust under measurement noise and interaction disorder.

Abstract

We demonstrate that weighted graph states (WGS) generated via variable-range interacting Ising spin systems where the interaction strength decays with distance as a power law, characterized by the fall-off rate, can successfully implement single- and two-qubit gates with fidelity exceeding classical limits by performing suitable measurements. In the regime of truly long-range interactions (small fall-off rate), optimizing over local unitary operations, while retaining the local measurement scheme in the original measurement-based quantum computation (MBQC) set-up, enables the scheme to achieve nonclassical average fidelities. Specifically, we identify a threshold fall-off rate of the interaction above which the fidelity of both universal single- and two-qubit gates consistently exceeds $90\%$ accuracy. Moreover, we exhibit that the gate-implementation protocol remains robust under two realistic imperfections -- noise in the measurement process, modeled via unsharp measurements, and disorder in the interaction strengths. These findings confirm WGS produced through long-range systems as a resilient and effective resource for MBQC.