Extended Quantum Computing Patterns

Transform a quantum state from one basis to another so that the next operation can be performed in a more suitable representation.

An algorithm contains an operation that is easier to express or apply in a basis different from the current one.

The transformation adds gates and may need to be reversed later. Approximate transformations can reduce circuit depth at the cost of accuracy.

Apply a unitary transformation that maps the state to the required basis. Examples include the quantum Fourier transform, the Hadamard transform, and quantum discrete cosine or sine transforms.

The state is represented in a basis suited to the next part of the computation.

Quantum Fourier transform, inverse quantum Fourier transform, Hadamard transform, quantum DCT, and quantum DST.

Uniform Superposition; Quantum Phase Estimation (QPE)

QFT implementations in Qiskit, PennyLane, and Classiq, and the DCT and DST routines provided by Classiq.