Benchmark

Quantum Approximate Counting

Quantum Amplitude Estimation (BHMT algorithm) · Optimization · Qiskit, Cirq

Benchmark based on the Brassard-Hoyer-Mosca-Tapp (BHMT) quantum counting algorithm, which estimates the number of marked items in an unstructured database with quadratic speedup over classical counting. Given N items with K marked, the algorithm estimates K to within relative error epsilon using O(1/epsilon * sqrt(N/K)) queries. A simplified variant achieves the same query complexity using only Grover iterations.

countingamplitude-estimationGroverquadratic-speedupalgorithm

Benchmark based on the Brassard-Hoyer-Mosca-Tapp (BHMT) quantum counting algorithm, which estimates the number of marked items in an unstructured database with quadratic speedup over classical counting. Given N items with K marked, the algorithm estimates K to within relative error epsilon using O(1/epsilon * sqrt(N/K)) queries. A simplified variant achieves the same query complexity using only Grover iterations.

Key Metrics
Query complexity
O(1/ε × √(N/K))
Speedup
Quadratic over classical
Why It Matters

Provides a simplified, practical variant of quantum counting that achieves optimal query complexity using only standard Grover iterations.

Hardware

Simulator / hardware-agnostic

Framework

Qiskit, Cirq

Sources
📄
Quantum Approximate Counting, Simplified
arxiv · accessed 2026-03-19
📄
Quantum Counting
arxiv · accessed 2026-03-19