Estimating truncation effects of quantum bosonic systems using sampling algorithms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910394297090048 |
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| author | Hanada, Masanori Liu, Junyu Rinaldi, Enrico Tezuka, Masaki |
| author_facet | Hanada, Masanori Liu, Junyu Rinaldi, Enrico Tezuka, Masaki |
| contents | To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08546 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Estimating truncation effects of quantum bosonic systems using sampling algorithms Hanada, Masanori Liu, Junyu Rinaldi, Enrico Tezuka, Masaki Quantum Physics Artificial Intelligence Machine Learning High Energy Physics - Lattice High Energy Physics - Theory To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations. |
| title | Estimating truncation effects of quantum bosonic systems using sampling algorithms |
| topic | Quantum Physics Artificial Intelligence Machine Learning High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2212.08546 |