TIMES-ADAPT: A Quantum algorithm for real-time evolution in low-energy subspaces using fixed-depth circuits

TL;DR

TIMES-ADAPT is a variational quantum algorithm that efficiently simulates real-time evolution within low-energy subspaces using fixed-depth circuits, enabling applications like wave packet dynamics and energy transport in spin systems.

Contribution

The paper introduces TIMES-ADAPT, a novel variational quantum algorithm that constructs fixed-depth circuits for real-time evolution in low-energy subspaces, improving simulation efficiency.

Findings

Successfully benchmarks on Heisenberg XXZ model.

Demonstrates effective wave packet evolution simulation.

Shows potential for energy transport studies.

Abstract

We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained unitary that diagonalizes the Hamiltonian in a subspace, we construct fixed-depth circuits for real-time evolution in the subspace, where time only enters as a circuit parameter. We present two versions of the algorithm depending on whether the initial state is specified in the energy eigenbasis or computational basis. We consider two important applications of our methods: wave packet evolution and energy transport in spin systems. We benchmark our algorithms using variants of the Heisenberg XXZ model.