Extended Quantum Computing Patterns

Simulate the time evolution of a quantum system governed by a Hamiltonian.

An algorithm must approximate the action of the time-evolution operator exp(-iHt) for a Hamiltonian H and an evolution time t.

Approximation error, circuit depth, the structure of the Hamiltonian, and the available qubits affect the choice of simulation method.

Decompose the Hamiltonian and approximate its evolution using a method such as a Trotter-Suzuki product formula, a linear combination of unitaries, or qubitization.

The circuit approximates the evolution of the input state under the selected Hamiltonian for the requested time.

First- and higher-order Trotter formulas, time-evolution templates, qubitization, and LCU-based simulation.

Linear Combination of Unitaries; Variational Quantum Eigensolver (VQE); Quantum Phase Estimation (QPE)

Time-evolution and Trotterization components in PennyLane, Qiskit Algorithms, and Classiq.