Quantum phase estimation
Quantum phase estimation is a quantum algorithm that estimates the eigenphase of a unitary operator given a corresponding eigenstate.
Quantum Programming in Depth
Quantum phase estimation is a quantum algorithm for estimating the eigenphase associated with an eigenvalue of a unitary operator, given a corresponding eigenstate.
- How it is used
- Serves as a subroutine for extracting an eigenphase from a prepared eigenstate and unitary.
- How deep it goes
- Derives phase kickback and inverse-QFT decoding, then implements and tests two-bit QPE in Qiskit and Q#.
- Examples
- Uses Z, INC, and T eigenstate pairs, plus two-bit Qiskit and Q# circuits with unit tests.
- What you can do after
- Build it from scratch as a two-bit circuit and test returned eigenphases against known unitary-eigenstate pairs.
Read how Quantum Programming in Depth explains quantum phase estimation →
Building Quantum Software with Python
A phase estimation circuit is a quantum circuit that generates a phase-encoded state from an eigenstate and a unitary transformation for estimating an eigenvalue phase.
- How it is used
- Serves as a building block for Shor’s algorithm, amplitude estimation, and quantum counting.
- How deep it goes
- Works through eigenstates, controlled circuit powers, IQFT decoding, and a reusable circuit function; defers advanced estimation methods.
- Examples
- Uses an RY(2θ) circuit, a prepared single-qubit eigenstate, three estimation qubits, and an encoded frequency of 4.7.
- What you can do after
- Build it from scratch as a circuit that converts an eigenvalue phase into a measured frequency estimate.
Read how Building Quantum Software with Python explains quantum phase estimation →
Related concepts
- phase kickbackuses · Phase kickback is a quantum effect in which a controlled operation transfers a phase associated with its target to the relative phase of the control-qubit state.
- eigenvaluemeasures · An eigenvalue is a scalar by which a linear transformation scales a corresponding nonzero eigenvector without changing its direction.
- eigenphaseuses · An eigenphase is the phase associated with an eigenvalue of a unitary operator, typically expressed as the angle of that eigenvalue on the complex unit circle.
- quantum countingused by · Quantum counting is a quantum algorithm that estimates the number of marked states in a search space using amplitude amplification and phase estimation.
- eigenvectoruses · An eigenvector is a nonzero vector that a linear transformation maps to a scalar multiple of itself.
- unitary transformationuses · A unitary transformation is a linear transformation that preserves inner products and therefore preserves vector norms and quantum measurement probabilities.
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