Fidelity Overhead for Nonlocal Measurements in Variational Quantum Algorithms

Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli 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 the 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 nonunit 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 groupings of commuting Pauli products. For a set of molecular electronic Hamiltonians, we confirm that the numbers of measurements in schemes using nonlocal qubit rotations are still lower than those in their local qubit rotation counterparts, even after accounting for uncertainties introduced by additional gates.

Automated summary

Measuring quantum observables by grouping terms that can be rotated to sums of Pauli z operators has been proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest, allowing for a fewer number of measurements by grouping more terms into measurable fragments. However, previous estimations did not take into account the nonunit fidelity of quantum gates implementing the additional transformations. Through a simple error model, it is confirmed that the number of measurements in schemes using nonlocal qubit rotations are still lower than those using local qubit rotations, even after accounting for uncertainties introduced by additional gates.