Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
Trotterization-based, iterative approaches to quantum simulation are limited to simulation times less than the coherence time of the quantum computer. This limits the utility of quantum simulations on near-term quantum computers. Here, we present a hybrid quantum-classical algorithm, called Variational Fast Forwarding (VFF), for decreasing the quantum circuit depth of quantum simulations. VFF seeks an approximate diagonalization of a simulation unitary and uses a constant number of gates, enabling longer simulations. We investigate the scaling of the VFF algorithm's errors and the limitations they impose on simulation times. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. Finally, we implement VFF on Rigetti's quantum computer to demonstrate simulation beyond the coherence time for simple one-qubit Hamiltonians.