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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2501.17863 |
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| _version_ | 1866915733252866048 |
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| author | Gaz, Emanuele Popov, Pavel P. Pardo, Guy Lewenstein, Maciej Hauke, Philipp Zohar, Erez |
| author_facet | Gaz, Emanuele Popov, Pavel P. Pardo, Guy Lewenstein, Maciej Hauke, Philipp Zohar, Erez |
| contents | In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes the matter and improves the efficiency of the hardware resources. We demonstrate it for the simplest non-Abelian group addressable with this procedure, $\mathbb{D}_8$, both in the cases of one (1D) and two (2D) spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the $\mathbb{D}_8$ lattice gauge theory onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device as the one developed in $\href{https://doi.org/10.1038/s41567-022-01658-0}{[Nat. Phys. 18, 1053 (2022)]}$. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem and reducing the amount of quantum resources. This can serve as a way of simulating lattice gauge theories in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\mathbb{D}_8$ Gaz, Emanuele Popov, Pavel P. Pardo, Guy Lewenstein, Maciej Hauke, Philipp Zohar, Erez High Energy Physics - Lattice Quantum Physics In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes the matter and improves the efficiency of the hardware resources. We demonstrate it for the simplest non-Abelian group addressable with this procedure, $\mathbb{D}_8$, both in the cases of one (1D) and two (2D) spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the $\mathbb{D}_8$ lattice gauge theory onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device as the one developed in $\href{https://doi.org/10.1038/s41567-022-01658-0}{[Nat. Phys. 18, 1053 (2022)]}$. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem and reducing the amount of quantum resources. This can serve as a way of simulating lattice gauge theories in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions. |
| title | Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\mathbb{D}_8$ |
| topic | High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2501.17863 |