Quantum Simulation of Open Quantum Systems Using Density-Matrix Purification

• URL: http://arxiv.org/abs/2207.07112v2
• Date: Fri, 15 Jul 2022 20:44:24 GMT
• Title: Quantum Simulation of Open Quantum Systems Using Density-Matrix Purification
• Authors: Anthony W. Schlimgen, Kade Head-Marsden, LeeAnn M. Sager-Smith, Prineha Narang and David A. Mazziotti
• Abstract summary: We present a general framework for OQSs where the system's $d times d$ density matrix is recast as a $d2$ wavefunction. We demonstrate this method on a two-level system in a zero temperature amplitude damping channel and a two-site quantum Ising model.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Electronic structure and transport in realistically-sized systems often require an open quantum system (OQS) treatment, where the system is defined in the context of an environment. As OQS evolution is non-unitary, implementation on quantum computers -- limited to unitary operations -- is challenging. We present a general framework for OQSs where the system's $d \times d$ density matrix is recast as a $d^{2}$ wavefunction which can be evolved by unitary transformations. This theory has two significant advantages over conventional approaches: (i) the wavefunction requires only an $n$-qubit, compared to $2n$-qubit, bath for an $n$-qubit system and (ii) the purification includes dynamics of any pure-state universe. We demonstrate this method on a two-level system in a zero temperature amplitude damping channel and a two-site quantum Ising model. Quantum simulation and experimental-device results agree with classical calculations, showing promise in simulating non-unitary operations on NISQ quantum devices.

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