Related papers: Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware

Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware

URL: http://arxiv.org/abs/2412.14544v1
Date: Thu, 19 Dec 2024 05:50:54 GMT
Title: Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware
Authors: Alexander Yosifov, Aditya Iyer, Daniel Ebler, Vlatko Vedral,
Abstract summary: Quantum homogenization is a reservoir-based quantum state approximation protocol. We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation. We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
Score: 42.52549987351643
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Abstract: Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically-equivalent ($\mathtt{SWAP}$)$^\alpha$ formulation. We then demonstrate its applicability on available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of $\mathtt{CNOT}$ and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed ($\mathtt{SWAP}$)$^\alpha$ quantum homogenization protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics.

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