Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Abstract

We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states. CONTENTS I. Introduction 1 II. Results 2 A. Quantum Phase Transitions 3 B. Groundstate Optimisation 3 C. Calculating and Optimising Overlaps 5 D. Quantum Dynamics 6 III. Discussion 7 IV. Methods 8 A. Fixed-point equations 8 B. Error Mitigation Strategies 8 References 9