# Quantum simulation of quantum channels in nuclear magnetic resonance

## TL;DR

This paper introduces an efficient NMR-based quantum simulation framework for quantum channels, utilizing a decomposition of non-unitary operators into unitary components, demonstrated through three key quantum channels.

## Contribution

The paper presents a novel method for simulating quantum channels in NMR by decomposing non-unitary operators into unitary parts with minimal ancillary qubits, and experimentally demonstrates this approach.

## Key findings

- Successfully simulated phase damping, amplitude damping, and depolarizing channels.
- Measured fidelity and von Neumann entropy for each channel.
- Experimental implementation using nuclear spins in liquid samples.

## Abstract

We propose and experimentally demonstrate an efficient framework for the quantum simulation of quantum channels in NMR. Our approach relies on the suitable decomposition of non-unitary operators in a linear combination of $d$ unitary ones, which can be then experimentally implemented with the assistance of a number of ancillary qubits that grows logarithmically in $d$. As a proof-of-principle demonstration, we realize the quantum simulation of three quantum channels for a single-qubit: phase damping (PD), amplitude damping (AD), and depolarizing (DEP) channels. For these paradigmatic cases, we measure key features, such as the fidelity of the initial state and the associated von Neuman entropy for a qubit evolving through these channels. Our experiments are carried out using nuclear spins in a liquid sample and NMR control techniques.