Quantum expectation-value estimation by computational basis sampling

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle the necessity a large number measurements for statistical convergence to meet requirements precision, such as chemical accuracy application chemistry computations. Here we propose algorithm estimate value based on its approximate expression weighted sum classically-tractable matrix elements with some modulation, where weight and modulation factors are evaluated by sampling appropriately prepared states computational basis computers. Each those applying unitary transformation consisting at most N CNOT gates, qubits, target state whose evaluated. Our expected require fewer than conventional methods required precision when concentrated particular states. We provide numerical comparisons our method existing ones measuring electronic ground energies (expectation Hamiltonians lowest-energy states) various small molecules. Numerical results show that can reduce numbers obtain targeted several orders magnitudes molecules concentrated. another route measure observables, which could accelerate