Overcoming the entanglement barrier with sampled tensor networks

TL;DR

This paper introduces a hybrid tensor-network/Monte-Carlo method that efficiently simulates one-dimensional quantum dynamics by bypassing the entanglement barrier, enabling polynomial-time expectation value calculations.

Contribution

The authors develop a novel TN-MC algorithm that contracts spatio-temporal tensor networks efficiently, overcoming the entanglement barrier in 1D quantum evolution simulations.

Findings

The method scales polynomially with time for local operator expectation values.

Generalized temporal entropies grow at most logarithmically, indicating controlled entanglement growth.

Identification of continuous dynamical quantum phase transitions (DQPTs).

Abstract

The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier} restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave function amplitudes can be contracted efficiently along the left-right (spatial) direction. Exploiting this structure, we develop a hybrid Tensor-Network/Monte-Carlo (TN-MC) algorithm that samples the wave function and evaluates expectation values of generic local operators with computational cost that scales only polynomially in time. The accurate contraction of the wave function amplitudes is a consequence of the favorable scaling with time of the generalised temporal entropies. We find that their real part either saturates or, at most, grows logarithmically with time, revealing new instances of continuous dynamical quantum phase transitions (DQPTs) which we characterize. Our results therefore show that, when computing expectation values of local operators, the entanglement barrier in one-dimensional Hamiltonian evolution can be bypassed with a TN-MC blend.