# Classical Simulation of Arbitrary Quantum Noise

## TL;DR

This paper introduces a classical simulation method for arbitrary quantum noise in one-qubit systems interacting with a quantum bath, using state-dependent random unitary evolutions to replicate complex quantum dynamics.

## Contribution

It presents a novel classical simulation approach for quantum noise that accounts for initial state dependencies and extends to mixed and correlated states.

## Key findings

- Classical model can simulate quantum dissipation, recurrence, and dephasing.
- Simulation uses random unitary evolutions dependent on initial states.
- Method applies to mixed states and non-product system-bath states.

## Abstract

I present an explicit classical simulation of arbitrary quantum noise for quantum models in which one qubit interacts with a quantum bath. The classical model simulates the interaction of the bath and the qubit by random unitary evolutions. I show that any arbitrary quantum dynamics, including quantum dissipation, recurrence, and dephasing, can be simulated classically when one allows the unitary operators in the classical model to depend on the initial state of the system and bath. For initial mixed states of the system and non-product states of the system and bath, I demonstrate that random unitary expansion is still possible, in terms of a set of pure states.