Exclusive-or encoded algebraic structure for efficient quantum dynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913367849959424 |
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| author | Broers, Lukas Mathey, Ludwig |
| author_facet | Broers, Lukas Mathey, Ludwig |
| contents | We propose a formalism that captures the algebraic structure of many-body two-level quantum systems, and directly motivates an efficient numerical method. This formalism is based on the binary representation of the enumeration-indices of the elements of the corresponding Lie algebra. The action of arbitrarily large elements of that algebra reduces to a few bit-wise exclusive-or operations. This formalism naturally produces sparse representations of many-body density operators, the size of which we control through a dynamic truncation method. We demonstrate how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes. We find that this approach to calculating quantum dynamics scales close to linearly with the number of non-zero components in the density operator. We refer to this exclusive-or represented quantum algebra as ORQA. As a proof of concept, we provide a numerical demonstration of this formalism by simulating quantum annealing processes for the maximum independent set problem for up to 22 two-level systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exclusive-or encoded algebraic structure for efficient quantum dynamics Broers, Lukas Mathey, Ludwig Other Condensed Matter Quantum Physics We propose a formalism that captures the algebraic structure of many-body two-level quantum systems, and directly motivates an efficient numerical method. This formalism is based on the binary representation of the enumeration-indices of the elements of the corresponding Lie algebra. The action of arbitrarily large elements of that algebra reduces to a few bit-wise exclusive-or operations. This formalism naturally produces sparse representations of many-body density operators, the size of which we control through a dynamic truncation method. We demonstrate how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes. We find that this approach to calculating quantum dynamics scales close to linearly with the number of non-zero components in the density operator. We refer to this exclusive-or represented quantum algebra as ORQA. As a proof of concept, we provide a numerical demonstration of this formalism by simulating quantum annealing processes for the maximum independent set problem for up to 22 two-level systems. |
| title | Exclusive-or encoded algebraic structure for efficient quantum dynamics |
| topic | Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2404.09312 |