  We show that the Variational Quantum-Classical Simulation algorithm admits a
finite circuit depth scaling collapse when targeting the critical point of the
transverse field Ising chain. The order parameter only collapses on one side of
the transition due to a slowdown of the quantum algorithm when crossing the
phase transition. In order to assess performance of the quantum algorithm and
compute correlations in a system of up to 752 qubits, we use techniques from
integrability to derive closed-form analytical expressions for expectation
values with respect to the output of the quantum circuit. We also reduce a
conjecture made by Ho and Hsieh about the exact preparation of the transverse
field Ising ground state to a system of equations.
