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 use entangled measurements, which might introduce additional gates between physically disconnected qubits that harm the performance. To solve this problem, we propose hardware-efficient entangled measurements (HEEMs), 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 required circuits 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 ${\mathrm{H}}_2\mathrm{O}$ molecule with classical simulators and quantum hardware using the variational quantum eigensolver with HEEM.

• Received 24 October 2022
• Accepted 25 July 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.034044