Quantum Primitives

The examples include Generalized Quantum Signal Processing (GQSP), enabling flexible polynomial transformations of block-encoded unitaries, as well as the Swap Test, a standard subroutine for estimating quantum state overlaps and the Hadamard test. Together, these primitives underpin a wide range of algorithms in Hamiltonian simulation, matrix functions, variational optimization, and quantum machine learning.

• Hadamard test - A basic quantum primitive, utilized to extract the real part of an expectation value of a unitary matrix.
• Generalized Quantum Signal Processing (GQSP) - A quantum algorithmic primitive that extends standard QSP, allowing one to block-encode arbitrary polynomials of unitary operations. Utilizing, Classiq's built-in module gqsp_phases, the generalized version removes restrictions that appear in QSP, providing a direct and flexible method for state preparation, phase function transformations and Hamiltonian simulation.
• Swap test - A quantum function that checks the overlap between two quantum states. Given two quantum registers of the same size, the function returns as output a single test qubit whose state encodes the overlap between the two inputs. The swap test is commonly employed as a subroutine in quantum variational and machine learning algorithms, such as quantum kernel method and neural networks.