Zou et al. (2024): Forecasting Future World Events with Neural Networks
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This quantum computing paper on permutation unitary decomposition appears mismatched with its title about forecasting world events; likely a catalog error, but may relate to AI safety through quantum computing applications for cryptography or AI model analysis.
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Abstract
Efficient decomposition of permutation unitaries is vital as they frequently appear in quantum computing. In this paper, we identify the key properties that impact the decomposition process of permutation unitaries. Then, we classify these decompositions based on the identified properties, establishing a comprehensive framework for analysis. We demonstrate the applicability of the presented framework through the widely used multi-controlled Toffoli gate, revealing that the existing decompositions in the literature belong to only three out of ten of the identified classes. Motivated by this finding, we propose transformations that can adapt a given decomposition into a member of another class, enabling resource reduction.
Summary
This paper addresses the efficient decomposition of permutation unitaries in quantum computing by establishing a comprehensive classification framework based on key properties that affect the decomposition process. The authors analyze existing decompositions of the multi-controlled Toffoli gate and find they represent only three of ten identified classes. They propose transformations to convert decompositions between classes, enabling optimization and resource reduction in quantum circuit implementations.
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| Page | Type | Quality |
|---|---|---|
| AI-Augmented Forecasting | Approach | 54.0 |
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# Classification and transformations of quantum circuit decompositions for permutation operations
Ankit Khandelwal†TCS Research, Tata Consultancy Services, India
Handy Kurniawan†Facultad de Informática, Universidad Complutense de Madrid, Spain
Shraddha Aangiras
Rashtreeya Vidyalaya Preuniversity College, India
Özlem Salehi
Institute of Theoretical and Applied Informatics, Polish Academy of
Sciences, Poland
QWorld Association, Tallinn, Estonia
Algorithmiq Ltd, Kanavakatu 3C 00160 Helsinki, Finland
Adam Glos
aglos@iitis.pl
Institute of Theoretical and Applied Informatics, Polish Academy of
Sciences, Poland
Algorithmiq Ltd, Kanavakatu 3C 00160 Helsinki, Finland
###### Abstract
Efficient decomposition of permutation unitaries is vital as they frequently appear in quantum computing. In this paper, we identify the key properties that impact the decomposition process of permutation unitaries. Then, we classify these decompositions based on the identified properties, establishing a comprehensive framework for analysis. We demonstrate the applicability of the presented framework through the widely used multi-controlled Toffoli gate, revealing that the existing decompositions in the literature belong to only three out of ten of the identified classes. Motivated by this finding, we propose transformations that can adapt a given decomposition into a member of another class, enabling resource reduction.
$\\dagger$$\\dagger$footnotetext: These authors contributed equally to this work
## 1 Introduction
The idea of quantum computers was first introduced in Feynman’s seminal paper in 1982 \[ [1](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib1 "")\]. Since then, quantum computing has evolved from a theoretical concept to a promising technology with numerous potential applications. The fundamental difference between classical and quantum computing lies in the way information is processed and manipulated. Quantum computers use the principles of quantum mechanics, like quantum superposition, to perform complex calculations faster than classical computers for certain tasks. Over the past few decades, many powerful quantum algorithms, both for fault-tolerant quantum computers \[ [2](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib2 ""), [3](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib3 "")\] and for noisy intermediate-scale quantum hardware \[ [4](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib4 ""), [5](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib5 ""), [6](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib6 "")\], have been proposed.
The plethora of developed algorithms is dedicated to classical problems like searching and combinatorial optimization. The best-known algorithm that falls into this class is Grover’s Search Algorithm \[ [2](https://ar5iv.labs.arxiv.org/html/2312.11644#bib.bib2 "")\], which relies on the utilization of an oracle to ‘mark’ the desired states within the search space. The oracle implementation usuall
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