Quantum expectation-value estimation by computational basis sampling

Understand

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms.

• A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations.
• Here we propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically-tractable matrix elements with some modulation, where the weight and modulation factors are evaluated by sampling appropriately prepared quantum states in the computational basis on quantum computers.
• Each of those states is prepared by applying a unitary transformation consisting of at most N CNOT gates, where N is the number of qubits, to a target quantum state whose expectation value is evaluated.