We’ve learned, in the previous video, how to record the phase that an eigenstate of a unitary picks up when that unitary is applied. But how do we determine what this phase is, given the probabilistic nature of quantum measurements? In this video, Ben will discuss the two different scenarios in which a relative phase has to be measured, and the two different methods which are specialised to deal with each scenario.

Main takeaways

• Due to the probabilistic nature of quantum measurement, it is necessary to prepare an input state multiple times in order to be able to learn the value of a phase with precision.
• Depending on whether the phase is produced by a quantum algorithm, it may be more efficient to apply phases of the form to an array of ancilla qubits which are prepared in special input states which are specifically tailored to get the most out of each quantum measurement.
• The procedure we use to measure phases with high precision is the inverse of the quantum Fourier transform.