Simulation of time evolution with the MERA

TL;DR

This paper introduces an efficient algorithm for simulating quantum time evolution using MERA, capable of handling large systems and extending to higher dimensions, with applications to critical Ising chains.

Contribution

It presents a novel MERA-based algorithm for time evolution that reduces computational cost and can be applied to large and higher-dimensional lattice systems.

Findings

Simulation cost scales as L log(L), reduced to log(L) for translation-invariant systems

Accurate ground state energies obtained via imaginary time evolution

Algorithm applicable to higher-dimensional lattice systems

Abstract

We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The cost of a simulation, which scales as L log(L), is reduced to log(L) when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.