Quantum computing critical exponents

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.

Automated summary

The study demonstrates a unique feature of the variational quantum-classical simulation algorithm when targeting the critical point of the transverse field Ising chain - a finite circuit depth scaling collapse. By leveraging techniques from integrability, closed form analytical expressions for expectation values with respect to the output of the quantum circuit are derived, allowing for the assessment of quantum algorithm performance and computation of correlations in systems of up to 752 qubits. Additionally, a conjecture regarding the exact preparation of the transverse field Ising ground state proposed by Ho and Hsieh is reduced to a system of equations.