Method for amplitude estimation with noisy intermediate-scale quantum computers

Abstract

Embodiments relate to a method for estimating an amplitude of a unitary operator U to within an error ε by using a quantum processor configurable to implement the unitary operator U on a quantum circuit. The quantum circuit has a maximum depth S can implement the unitary operator no more than D times in a single run. A schedule of iterations n=1 to N based on the error ε and number D is determined. Each iteration n characterized by a schedule parameter kn. kn≤D for all n and kn increases at a rate that is less than exponential. The iterations n may be sequentially executed. In each iteration, the quantum processor is configured to sequentially apply and execute the unitary operator U kn times on the quantum circuit. A non-quantum processor then estimates the amplitude of the unitary operator U based on the measured resulting states.