Optimum phase estimation with two control qubits

Understand

Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems.

• When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is not possible to measure the phase with a minimum mean-square error.
• In standard methods, there would be a logarithmic (in error) number of control qubits needed in order to achieve this minimum error.
• Here show how to perform this measurement using only two control qubits, thereby reducing the qubit requirements of the quantum algorithm.