Quantum Rational Transformation Using Linear Combinations of Hamiltonian Simulations Article Swipe
Yizhi Shen
,
Niel Van Buggenhout
,
Daan Camps
,
Katherine Klymko
,
Roel Van Beeumen
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.07742
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.07742
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a target operator on quantum hardware. By leveraging suitable integral representations of the operator resolvent, we show that rational transformations can be performed efficiently with Hamiltonian simulations using a linear-combination-of-unitaries (LCU). We formulate two complementary LCU approaches, discrete-time and continuous-time LCU, each providing unique strategies to decomposing the exact integral representations of a resolvent. We consider quantum rational transformation for the ubiquitous task of approximating functions of a Hermitian operator, with particular emphasis on the elementary signum function. For illustration, we discuss its application to the ground and excited state problems. Combining rational transformations with observable dynamic mode decomposition (ODMD), our recently developed noise-resilient quantum eigensolver, we design a fully real-time approach for resolving many-body spectra. Our numerical demonstration on spin systems indicates that our real-time framework is compact and achieves accurate estimation of the low-lying energies.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2408.07742
- https://arxiv.org/pdf/2408.07742
- OA Status
- green
- Related Works
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- OpenAlex ID
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https://openalex.org/W4406022260Canonical identifier for this work in OpenAlex
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https://doi.org/10.48550/arxiv.2408.07742Digital Object Identifier
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Quantum Rational Transformation Using Linear Combinations of Hamiltonian SimulationsWork title
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preprintOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-08-14Full publication date if available
- Authors
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Yizhi Shen, Niel Van Buggenhout, Daan Camps, Katherine Klymko, Roel Van BeeumenList of authors in order
- Landing page
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https://arxiv.org/abs/2408.07742Publisher landing page
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https://arxiv.org/pdf/2408.07742Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2408.07742Direct OA link when available
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Hamiltonian (control theory), Transformation (genetics), Quantum, Mathematics, Statistical physics, Mathematical physics, Physics, Applied mathematics, Quantum mechanics, Mathematical optimization, Chemistry, Gene, BiochemistryTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |