Extended Quantum Computing Patterns

Estimate the probability of measuring a selected outcome in a quantum state.

A quantum algorithm prepares a state containing a target outcome whose probability must be estimated, as in Monte Carlo integration, risk analysis, or option pricing.

Canonical amplitude estimation uses phase estimation and additional qubits. Iterative and maximum-likelihood variants reduce the number of ancillas but require repeated circuit executions.

Construct an operator that amplifies the target subspace and estimate the amplitude either with quantum phase estimation or with an iterative or likelihood-based procedure.

The probability of the selected outcome is estimated. Under suitable assumptions, amplitude estimation offers a quadratic improvement in sampling complexity over classical Monte Carlo estimation.

Canonical QAE, iterative QAE, maximum-likelihood amplitude estimation, and faster amplitude estimation.

Amplitude Amplification; Quantum Phase Estimation (QPE); Domain Specific Application

Amplitude-estimation components in Qiskit Algorithms and finance applications such as option pricing and risk estimation.