Quantum simulation of quantum channels in nuclear magnetic resonance

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.

8 pages, 7 figures, All comments are welcome

References in corpus (10)

• An Open-System Quantum Simulator with Trapped Ions
• Liquid State NMR as a Test-bed for Developing Quantum Control Methods
• Binary search trees for generalized measurement
• Quantum Channel Construction with Circuit Quantum Electrodynamics
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Quantum Simulation of Dissipative Processes without Reservoir Engineering
• Quantum Circuits for Quantum Channels
• Projective measurement in nuclear magnetic resonance
• Quantum and classical resources for unitary design of open-system evolutions
• Measurement of linear response functions in Nuclear Magnetic Resonance

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