Quantum computing critical exponents
Henrik Dreyer, Mircea Bejan, Etienne Granet · Physical Review A · 2021
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 [W. W. Ho and T. H. Hsieh, SciPost Phys. 6, 029 (2019)] about the exact preparation of the transverse field Ising ground state to a system of equations.