Simulability transitions in continuous-time dynamics of local open quantum systems

TL;DR

This paper investigates the classical simulability of continuous-time local quantum spin systems under noise, showing efficient algorithms at high noise levels and hardness results at low noise, depending on the regime.

Contribution

It establishes a threshold for efficient classical simulation based on noise rate and encodes quantum computations to demonstrate simulation hardness in low-noise regimes.

Findings

Polynomial-time classical sampling above noise threshold

Hardness of simulation in low-noise regimes for certain channels

Encoding of quantum computations into spin dynamics

Abstract

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to sample from the state of the spins when the rate of noise is higher than a threshold determined by the strength of the local interactions. Furthermore, by encoding a 1D fault tolerant quantum computation into the dynamics of spin systems arranged on two or higher dimensional grids, we show that for several noise channels, the problem of weakly simulating the output state of both purely Hamiltonian and purely dissipative dynamics is expected to be hard in the low-noise regime.