Quantum-to-Classical Computability Transition via Negative Markov Chains

TL;DR

This paper introduces a framework using negative Markov chains to analyze quantum dynamics, showing how noise can induce a transition to classical simulability by suppressing quantum complexity.

Contribution

It develops a novel representation of quantum dynamics via negative Markov chains and demonstrates how noise can induce a transition to classical behavior in quantum systems.

Findings

Quantum complexity arises from particle proliferation in the Markov process.

Noise can suppress particle growth, making classical simulation feasible.

A critical noise threshold exists for classicalizing open quantum spin chains.

Abstract

We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation and sampling intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing particle growth and making Monte Carlo sampling efficient. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold which can be efficiently determined for any model.