Abstract: Methods, systems, and apparatus for verified quantum phase estimation. In one aspect, a method includes repeatedly performing a experiment. Performing one repetition of the experiment includes: applying a second unitary to a system register of N qubits prepared in a target computational basis state; applying, conditioned on a state of a control qubit, a first unitary to the system register; applying an inverse of the second unitary to the system register and measuring each qubit to determine an output state of the system register; measuring the control qubit to obtain a corresponding measurement result m; and post-selecting on the target computational basis state by, in response to determining that the output state indicates that each qubit was in the target computational basis state prior to measurement, incrementing a first or second classical variable by (?1)m. Phases or expectation values of the first unitary are estimated based on the classical variables.