Quantum Phase Estimation

Quantum Phase Estimation

Quantum Phase Estimation (QPE) is one of the most important subroutines in quantum computing, sitting at the heart of Shor's factoring algorithm, the HHL linear-systems solver, and quantum simulation of chemistry and materials. Given a unitary operator and one of its eigenstates, QPE estimates the corresponding eigenvalue's phase, the angle theta for which the eigenvalue is exp(2pii*theta), to a precision set by the number of ancilla qubits used. This Cirq example builds and simulates a phase-estimator circuit that recovers an unknown phase encoded in a target qubit: it prepares a register of ancilla qubits in superposition, applies a sequence of controlled powers of the unitary so that the phase is kicked back into the ancilla register, and then applies an inverse quantum Fourier transform to convert the accumulated relative phases into a binary readout of theta. Measuring the ancillas yields an estimate of the phase whose accuracy improves with each additional qubit. The script lets you vary the number of estimation qubits to see the precision-versus-resources tradeoff directly. It is a clear, hands-on introduction to the phase-estimation primitive that so many advanced quantum algorithms are built upon.

Run it

pip install -r requirements.txt
python phase_estimator.py

Source and license

Imported from examples/phase_estimator.py in quantumlib/Cirq at v1.6.1, under the Apache License 2.0. Original authors: The Cirq Developers. The upstream LICENSE is included alongside this example.