Many quantum algorithms involve applying a unitary operator to one of its eigenstates, resulting in a phase being applied to the input state. For example, Shor’s factoring algorithm and Grover’s search algorithm both involve this step. There is a surprisingly simple trick for reading these phases out, which Ben will introduce to you here.

Main takeaways

• An operator U, applied to one of its eigenstates |ψ⟩, results in a state eiϕ|ψ⟩. Normally, such a global phase produces no measurable effect.
• Using a single ancilla qubit, we can turn this global phase into a relative phase, whose influence on an input state can be measured.