quantum phase estimation

Quantum Phase Estimation (QPE) is an algorithm that determines the eigenvalues, or phase, of a unitary operator. It leverages quantum superposition and interference to extract this phase information with exponential precision compared to classical algorithms.

QPE is a foundational subroutine for many advanced quantum algorithms, including Shor's algorithm for factoring large numbers. By efficiently estimating phases, it unlocks solutions to complex problems in chemistry, materials science, and cryptography.

The algorithm heavily relies on the Quantum Fourier Transform (QFT) to extract the phase from the quantum state. The QFT allows the algorithm to translate the phase information from the amplitudes of the quantum state into a readable binary format.

The number of qubits required depends on the desired precision of the estimated phase, typically requiring 'n' qubits for 'n' bits of precision. It operates by using two registers, one for the eigenstate and one to store the resulting phase value.