  The scaling of the entanglement entropy at a quantum critical point allows us
to extract universal properties of the state, e.g., the central charge of a
conformal field theory. With the rapid improvement of noisy intermediate-scale
quantum (NISQ) devices, these quantum computers present themselves as a
powerful tool to study critical many-body systems. We use finite-depth quantum
circuits suitable for NISQ devices as a variational ansatz to represent ground
states of critical, infinite systems. We find universal finite-depth scaling
relations for these circuits and verify them numerically at two different
critical points, i.e., the critical Ising model with an additional
symmetry-preserving term and the critical XXZ model.
