Quantum amplitude amplification and estimation

Gilles Brassard; Peter Høyer; Michele Mosca; Alain Tapp

doi:10.1090/conm/305/05215

qcr:2606.64149.1

Quantum amplitude amplification and estimation

Gilles Brassard, Peter Høyer, Michele Mosca, +1 more

Implementation of the original Quantum Amplitude Estimation (QAE) algorithm introduced by Brassard, Hoyer, Mosca, and Tapp in 2000. Given a unitary A that prepares a superposition with an unknown "good state" amplitude a, the algorithm estimates a with quadratic speedup over classical sampling. It works by applying Quantum Phase Estimation (QPE) to the Grover operator, whose eigenvalues encode the target amplitude. The raw QPE output lands on a discrete grid of 2^m points (where m is the number of evaluation qubits), so a Maximum Likelihood Estimation (MLE) post-processing step refines the result to a continuous value without additional quantum resources. This example demonstrates the algorithm on a Bernoulli model, the simplest amplitude estimation problem, estimating a target probability of 0.2 using 3 evaluation qubits. The implementation includes Fisher information confidence intervals and likelihood-ratio confidence intervals for statistical rigour.

10.1090/conm/305/05215

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