  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.
