Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer

TL;DR

This paper demonstrates the first fully optimized variational quantum simulation of a dynamical quantum phase transition in the transverse field Ising model on a trapped-ion quantum computer, showcasing the potential of variational methods for complex quantum dynamics.

Contribution

It introduces a variational quantum time-evolution approach using a quantum circuit matrix product state ansatz optimized with a fidelity cost function, tailored for current quantum hardware.

Findings

Successfully simulated dynamical quantum phase transition on a trapped-ion device.

Showed that variational quantum algorithms can handle delicate phase cancellations in many-body systems.

Revealed a hidden simplicity in the evolution of the transverse-field Ising model during the phase transition.

Abstract

We time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.