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.
@article{arxiv.2104.01168,
title = {Quantum computing critical exponents},
author = {Henrik Dreyer and Mircea Bejan and Etienne Granet},
journal= {arXiv preprint arXiv:2104.01168},
year = {2022}
}