Fidelity overhead for non-local measurements in variational quantum algorithms

TL;DR

This paper analyzes how non-local measurements in variational quantum algorithms are affected by gate fidelity, showing that despite added uncertainties, non-local schemes still require fewer measurements for molecular Hamiltonians.

Contribution

It introduces a model for gate errors in non-local measurement schemes and demonstrates their effectiveness remains superior despite fidelity reductions.

Findings

Non-local measurement schemes require fewer measurements than local schemes.

Gate errors increase measurement counts but do not negate the advantages of non-local schemes.

Non-local schemes outperform local schemes even with realistic gate fidelity limitations.

Abstract

Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli $\hat z$ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest so that the measurement of a fragment's Ising form would be equivalent to measurement of the fragment for the unrotated state. These extra rotations allow one to perform a fewer number of measurements by grouping more terms into the measurable fragments with a lower overall estimator variance. However, previous estimations of the number of measurements did not take into account non-unit fidelity of quantum gates implementing the additional transformations. Through a circuit fidelity reduction, additional transformations introduce extra uncertainty and increase the needed number of measurements. Here we consider a simple model for errors introduced by additional gates needed in schemes involving grouping of commuting Pauli products. For a set of molecular electronic Hamiltonians, we confirm that the numbers of measurements in schemes using non-local qubit rotations are still lower than those in their local qubit rotation counterparts, even after accounting for uncertainties introduced by additional gates.