Variational dynamics as a ground-state problem on a quantum computer

TL;DR

This paper introduces a variational quantum algorithm that encodes quantum dynamics as a ground-state problem, enabling the study of real-time evolution and phase transitions in quantum systems using a quantum computer.

Contribution

It presents a novel approach to simulate quantum dynamics by mapping it onto a ground-state problem with a variational method, leveraging the Feynman-Kitaev Hamiltonian.

Findings

Favorable scaling with the number of qubits and gates.

Robustness against noise demonstrated through numerical experiments.

Effective detection of dynamical quantum phase transitions.

Abstract

We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits. We prepare the Feynman-Kitaev Hamiltonian acting on the composed system as a qubit operator and find an approximate ground state using the Variational Quantum Eigensolver. We apply the algorithm to the study of the dynamics of a transverse field Ising chain with an increasing number of spins and time steps, proving a favorable scaling in terms of the number of two qubit gates. Through numerical experiments, we investigate its robustness against noise, showing that the method can be use to evaluate dynamical properties of quantum systems and detect the presence of dynamical quantum phase transitions by measuring Loschmidt echoes.