Local fermion-to-qudit mappings: a practical recipe for four-level systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908553229369344 |
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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 |