Quantum real-time evolution using tensor renormalization group methods

TL;DR

This paper presents a novel tensor renormalization group approach for approximate real-time evolution of quantum systems, demonstrating effectiveness in 1+1D models and discussing potential for quantum computer benchmarking.

Contribution

It introduces a HOTRG-based method for real-time quantum evolution, extending TRG techniques from imaginary to real time, and evaluates its performance on the Transverse Ising Model.

Findings

Effective in evolving Gaussian wave packets in disordered phase

More challenging near criticality

Potential for benchmarking quantum computers

Abstract

We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time evolution operator for a 1+1D Transverse Ising Model with a longitudinal field. We show that it is effective and efficient in evolving Gaussian wave packets for one and two particles in the disordered phase. Near criticality behavior is more challenging in real-time. We compare our algorithm with local simulators for universal quantum computers and discuss possible benchmarking in the near future.