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arXiv · 2306.00795

Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective

Allan Tosta·Antônio C. Lourenço·Daniel Brod·Fernando Iemini·Tiago Debarba
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Abstract

Quantum computational models can be approached via the lens of resources needed to perform computational tasks, where a computational advantage is achieved by consuming specific forms of quantum resources, or, conversely, resource-free computations are classically simulable. Can we similarly identify quantum computational resources in the setting of more general quasi-particle statistics? In this work, we develop a framework to characterize the separability of a specific type of one-dimensional quasiparticle known as a fermionic anyon. As we evince, the usual notion of partial trace fails in this scenario, so we build the notion of separability through a fractional Jordan-Wigner transformation, leading to an entanglement description of fermionic-anyon states. We apply this notion of fermionic-anyon separability, and the unitary operations that preserve it, mapping it to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons.

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Allan Tosta, Antônio C. Lourenço, Daniel Brod, Fernando Iemini, Tiago Debarba. 2023-06-01. Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective. https://doi.org/10.1103/physreva.110.l010404

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