Extended Quantum Computing Patterns

Represent an operator as a weighted sum of simpler unitary operators that can be implemented on a quantum computer.

An algorithm must apply an operator that is not directly unitary but can be decomposed into a weighted sum of available unitary operations.

The method requires ancilla qubits and state-preparation and selection operations. Its cost depends on the number and weights of the component unitaries.

Prepare an ancilla state containing the coefficients, apply each component unitary under ancilla control, and combine the branches so that the target operator appears in a selected subspace.

The weighted operator is embedded in a larger unitary operation and can be used as a building block in other algorithms.

Block encoding, PREPARE-SELECT-PREPARE constructions, qubitization, and singular-value transformation routines.

Hamiltonian Simulation; Amplitude Amplification

LCU and block-encoding components in Classiq and PennyLane.