  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 of the 1+1 dimensional $\lambda \phi^4$ quantum field theory
including encoding, state preparation, and time evolution, with several
numerical simulation results. These algorithms could be understood as near-term
variational quantum circuit (quantum neural network) analogs of the
Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field
theory using universal quantum devices. Besides, we highlight the advantages of
encoding with harmonic oscillator basis based on the LSZ reduction formula and
several computational efficiency such as when implementing a bosonic version of
the unitary coupled cluster ansatz to prepare initial states. We also discuss
how to circumvent the "spectral crowding" problem in the quantum field theory
simulation and appraise our algorithm by both state and subspace fidelities.
