Local fermion-to-qudit mappings: a practical recipe for four-level systems

Fuente: arXiv
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Auteurs principaux: Carobene, Rodolfo, Barison, Stefano, Giachero, Andrea, Nys, Jannes
Format: Preprint
Publié: 2024
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author Carobene, Rodolfo
Barison, Stefano
Giachero, Andrea
Nys, Jannes
author_facet Carobene, Rodolfo
Barison, Stefano
Giachero, Andrea
Nys, Jannes
contents In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner transformation (JWT), while useful, often result in non-local operators that scale unfavorably with system size. To address these challenges, we introduce mappings that efficiently localize fermionic operators on qudits, reducing the non-locality and operator weights associated with JWT. We propose one mapping for spinless fermions and two mappings for spinful fermions, comparing their performance in terms of qudit-weight, circuit depth, and gate complexity. By leveraging the extended local Hilbert space of qudits, we show that these mappings enable more efficient quantum simulations in terms of two-qudit gates, reducing hardware requirements without increasing computational complexity. We validate our approach by simulating prototypical models such as the spinless t-V model and the Fermi-Hubbard model in two dimensions, using Trotterized time evolution. Our results highlight the potential of qudit-based quantum simulations in achieving scalability and efficiency for fermionic systems on near-term quantum devices.
format Preprint
id arxiv_https___arxiv_org_abs_2412_05616
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Local fermion-to-qudit mappings: a practical recipe for four-level systems
Carobene, Rodolfo
Barison, Stefano
Giachero, Andrea
Nys, Jannes
Quantum Physics
Materials Science
Chemical Physics
Computational Physics
In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner transformation (JWT), while useful, often result in non-local operators that scale unfavorably with system size. To address these challenges, we introduce mappings that efficiently localize fermionic operators on qudits, reducing the non-locality and operator weights associated with JWT. We propose one mapping for spinless fermions and two mappings for spinful fermions, comparing their performance in terms of qudit-weight, circuit depth, and gate complexity. By leveraging the extended local Hilbert space of qudits, we show that these mappings enable more efficient quantum simulations in terms of two-qudit gates, reducing hardware requirements without increasing computational complexity. We validate our approach by simulating prototypical models such as the spinless t-V model and the Fermi-Hubbard model in two dimensions, using Trotterized time evolution. Our results highlight the potential of qudit-based quantum simulations in achieving scalability and efficiency for fermionic systems on near-term quantum devices.
title Local fermion-to-qudit mappings: a practical recipe for four-level systems
topic Quantum Physics
Materials Science
Chemical Physics
Computational Physics
url https://arxiv.org/abs/2412.05616