Towards a variational Jordan-Lee-Preskill quantum algorithm

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation, explicitly designed for quantum simulation of quantum field theory. We develop hybrid quantum-classical algorithms for crucial ingredients in particle scattering experiments, including encoding, state preparation, and time evolution, with several numerical simulations to demonstrate our algorithms in the 1+1 dimensional $\lambda \phi^4$ quantum field theory. These algorithms could be understood as near-term analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Our contribution also includes a bosonic version of the Unitary Coupled Cluster ansatz with physical interpretation in quantum field theory, a discussion about the subspace fidelity, a comparison among different bases in the 1+1 dimensional $\lambda \phi^4$ theory, and the "spectral crowding" in the quantum field theory simulation.