Quantum computing critical exponents

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.

16 pages, 5 figures

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• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• A simple theory for quantum quenches in the ANNNI model
• Characterization of variational quantum algorithms using free fermions
• Exact mean-field solution of a spin chain with short-range and long-range interactions
• Finite-depth scaling of infinite quantum circuits for quantum critical points
• Sketching phase diagrams using low-depth variational quantum algorithms
• Learning quantum phases via single-qubit disentanglement