Quantum computing critical exponents

TL;DR

This paper demonstrates that a variational quantum-classical algorithm exhibits a finite-depth scaling collapse at the critical point of the transverse field Ising model, revealing insights into quantum phase transitions and algorithm performance.

Contribution

It introduces a finite circuit depth scaling analysis at criticality and derives analytical expressions for expectation values in large systems, advancing understanding of quantum algorithms near phase transitions.

Findings

Order parameter collapse on one side of the transition

Analytical expressions for expectation values in large systems

Reduction of a conjecture about ground state preparation

Abstract

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.