Tangible reduction in learning sample complexity with large classical samples and small quantum system

Song, Wooyeong; Wieśniak, Marcin; Liu, Nana; Pawłowski, Marcin; Lee, Jinhyoung; Kim, Jaewan; Bang, Jeongho

doi:10.1007/s11128-021-03217-7

Cited by 4 publications

(7 citation statements)

References 30 publications

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“…Finally, from a viewpoint of quantum information, the concept of embedding is closely related to entanglement. Understanding the connection between the performance of quantum embedding algorithms and fragment-bath entanglement entropy may provide a general way to describe and understand the complexity of chemical and physical problems from a quantum information perspective. − Current quantum computers are smallwe believe our quantum bootstrap embedding method provides a general strategy to use multiple small quantum machines to solve large problems in chemistry and beyond. , We look forward to future development in these directions.…”

Section: Discussionmentioning

confidence: 99%

“…105−107 Current quantum computers are small�we believe our quantum bootstrap embedding method provides a general strategy to use multiple small quantum machines to solve large problems in chemistry and beyond. 108,109 We look forward to future development in these directions. Note that approximate QES are likely to achieve exponential speedup as compared to classical FCI solver.…”

Section: Additional Quadratic Speedup In Accuracymentioning

confidence: 99%

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Bootstrap Embedding on a Quantum Computer

Liu

Chin

Dutt

et al. 2023

J. Chem. Theory Comput.

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We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match�at little additional computational cost�full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

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Section: Discussionmentioning

confidence: 99%

Section: Additional Quadratic Speedup In Accuracymentioning

confidence: 99%

Bootstrap Embedding on a Quantum Computer

Liu

Chin

Dutt

et al. 2023

J. Chem. Theory Comput.

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“…In particular, theoretical and empirical evidence exists for improvements in generalization error [137,[203][204][205], trainability (i.e. with certain constructions, favourable training landscapes with fewer barren plateaus and narrow gorges [137,203,[206][207][208][209]), and sample complexity [210][211][212]. It is plausible that these types of advantages may lead to novel machine learning applications in biology and medicine.…”

Section: Variational Quantum Machine Learningmentioning

confidence: 99%

“…Many of the quantum advantages associated with near-term variational QML algorithms relate to model capacity, expressivity and sample efficiency. In particular, variational QML algorithms may yield reductions in the number of required trainable parameters [ 214 ], generalization error [ 137 , 203 – 205 ], the number of examples required to learn a model [ 199 , 212 ] and improvements in training landscapes [ 137 , 199 , 203 , 207 , 208 , 252 ]. Evidence supporting one or more of these advantages has been found in both theoretical models and proof of principle implementations of quantum neural networks (QNNs) [ 137 , 203 , 204 , 207 ] and quantum kernel methods (QKMs) [ 199 , 201 , 205 ].…”

Section: Future Prospects In Biology and Medicinementioning

confidence: 99%

“…If such sample complexity advantages are achievable with classical data, they will likely be problem instance specific [ 201 ], highly dependent on the distribution of the input data [ 199 , 201 ] and are unlikely to be superpolynomial [ 211 , 395 ]. Nonetheless, polynomial [ 210 – 212 ] or even sub-linear reductions in the number of examples required to build a classifier could provide significant operational advantages…”

Section: Future Prospects In Biology and Medicinementioning

confidence: 99%

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Biology and medicine in the landscape of quantum advantages

Cordier

Sawaya

Guerreschi

et al. 2022

J. R. Soc. Interface.

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Quantum computing holds substantial potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning methods for subtyping cancers on the basis of clinical features. This potential is encapsulated by the concept of a quantum advantage, which is contingent on a reduction in the consumption of a computational resource, such as time, space or data. Here, we distill the concept of a quantum advantage into a simple framework to aid researchers in biology and medicine pursuing the development of quantum applications. We then apply this framework to a wide variety of computational problems relevant to these domains in an effort to (i) assess the potential of practical advantages in specific application areas and (ii) identify gaps that may be addressed with novel quantum approaches. In doing so, we provide an extensive survey of the intersection of biology and medicine with the current landscape of quantum algorithms and their potential advantages. While we endeavour to identify specific computational problems that may admit practical advantages throughout this work, the rapid pace of change in the fields of quantum computing, classical algorithms and biological research implies that this intersection will remain highly dynamic for the foreseeable future.

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Complexity of life sciences in quantum and AI era

Pyrkov,

Aliper,

Bezrukov

et al. 2024

WIREs Comput Mol Sci

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Having made significant advancements in understanding living organisms at various levels such as genes, cells, molecules, tissues, and pathways, the field of life sciences is now shifting towards integrating these components into the bigger picture to understand their collective behavior. Such a shift of perspective requires a general conceptual framework for understanding complexity in life sciences which is currently elusive, a transition being facilitated by large‐scale data collection, unprecedented computational power, and new analytical tools. In recent years, life sciences have been revolutionized with AI methods, and quantum computing is touted to be the next most significant leap in technology. Here, we provide a theoretical framework to orient researchers around key concepts of how quantum computing can be integrated into the study of the hierarchical complexity of living organisms and discuss recent advances in quantum computing for life sciences.This article is categorized under: Data Science > Artificial Intelligence/Machine Learning Quantum Computing > Algorithms Structure and Mechanism > Computational Biochemistry and Biophysics

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Tangible reduction in learning sample complexity with large classical samples and small quantum system

Cited by 4 publications

References 30 publications

Bootstrap Embedding on a Quantum Computer

Bootstrap Embedding on a Quantum Computer

Biology and medicine in the landscape of quantum advantages

Complexity of life sciences in quantum and AI era

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