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arXiv · 2412.14544

Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware

Alexander Yosifov·Aditya Iyer·Daniel Ebler·Vlatko Vedral
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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 ($\mathtt{SWAP}$)$^α$ 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 ($\mathtt{SWAP}$)$^α$ 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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Alexander Yosifov, Aditya Iyer, Daniel Ebler, Vlatko Vedral. 2024-12-19. Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware. https://arxiv.org/abs/2412.14544

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