Hardware-efficient entangled measurements for variational quantum algorithms

TL;DR

This paper introduces hardware-efficient entangled measurements (HEEM) for variational quantum algorithms, reducing circuit count and depth by limiting entanglement to physically connected qubits, thus improving performance on NISQ devices.

Contribution

The paper proposes HEEM, a measurement scheme that enhances variational algorithms by optimizing entanglement to only physically connected qubits, improving efficiency on NISQ hardware.

Findings

HEEM reduces the number of circuits needed for Hamiltonian evaluation.

HEEM improves accuracy over local and arbitrarily entangled measurements.

Experimental results demonstrate effective ground-state energy estimation for H$_2$O.

Abstract

Variational algorithms have received significant attention in recent years due to their potential to solve practical problems using noisy intermediate-scale quantum (NISQ) devices. A fundamental step of these algorithms is the evaluation of the expected value of Hamiltonians, and hence efficient schemes to perform this task are required. The standard approach employs local measurements of Pauli operators and requires a large number of circuits. An alternative is to make use of entangled measurements, which might introduce additional gates between physically disconnected qubits that harm the performance. As a solution to this problem, we propose hardware-efficient entangled measurements (HEEM), that is, measurements that permit only entanglement between physically connected qubits. We show that this strategy enhances the evaluation of molecular Hamiltonians in NISQ devices by reducing the number of circuits required without increasing their depth. We provide quantitative metrics of how this approach offers better results than local measurements and arbitrarily entangled measurements. We estimate the ground-state energy of the H$_2$O molecule with classical simulators and quantum hardware using the variational quantum eigensolver with HEEM.