Directly estimating the fidelity of measurement-based quantum computation

TL;DR

This paper establishes a direct relationship between the fidelity of noisy resource states and the actual performance of measurement-based quantum computation, providing a practical method to estimate computational fidelity.

Contribution

It derives an exact expression linking MBQC fidelity to a correlation function and introduces an efficient way to directly estimate MBQC fidelity from noisy states.

Findings

State fidelity is a tight lower bound on MBQC fidelity.

State fidelity can underestimate MBQC performance significantly.

A new method for directly estimating MBQC fidelity from correlation measurements.

Abstract

In measurement-based quantum computation (MBQC), quantum circuits are implemented using adaptive measurements on an entangled resource state. In practice, the resource state will always be prepared with some noise, and it is crucial to understand the effect of this noise on the operation of MBQC. Typically, one measures the fidelity of the noisy resource state with the assumption that a high fidelity state means a high fidelity computation. However, the precise relationship between these two fidelities is not known. Here, we derive an expression that equates the average fidelity of the MBQC output state to a certain correlation function evaluated on the noisy resource state. Using this expression, we show that state fidelity provides a tight lower bound on average MBQC fidelity. Conversely, we also find that state fidelity can greatly underestimate average MBQC fidelity, implying that state fidelity is not a good indicator of MBQC performance in general. In response, we formulate an efficient method to directly estimate average MBQC fidelity by measuring the aforementioned correlation function. These results therefore improve our ability to characterize noisy resource states in quantum computers and benchmark MBQC performance.