Propagators

Propagators implement the unitary time evolution for different types of operators. Choose the appropriate propagator based on your operator’s structure.

Table 1 Propagator Selection Guide

Propagator	Use When	Example Applications
Circulant	Operator is circulant (translation-invariant)	QWOA, constrained combinatorial optimisation
Diagonal	Operator is diagonal in computational basis	Phase operators, cost Hamiltonians
Sparse	Operator is a general sparse matrix	QAOA, custom Hamiltonians
Composite	Operator is a Cartesian sum of circulant operators mixing over subregisters	Discretised continuous multivariable optimisation, combinatorial problems with decision variables of arity ≥ 3
Momentum	State evolves in momentum space	Gradient-descent search inspired by continuous-variable photonic quantum computing

• Circulant
• Diagonal
• Sparse
• Composite
• Momentum