  We present a quantum-classical algorithm to study the dynamics of the
two-spatial-site Schwinger model on IBM's quantum computers. Using rotational
symmetries, total charge, and parity, the number of qubits needed to perform
computation is reduced by a factor of $\sim 5$, removing exponentially-large
unphysical sectors from the Hilbert space. Our work opens an avenue for
exploration of other lattice quantum field theories, such as quantum
chromodynamics, where classical computation is used to find symmetry sectors in
which the quantum computer evaluates the dynamics of quantum fluctuations.
