Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TLDR
In this paper, the authors considered factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems.Abstract:
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed to be able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, for example, the number of digits of the integer to be factored.read more
Citations
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Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future as mentioned in this paper, which will be useful tools for exploring many-body quantum physics, and may have other useful applications.
Journal ArticleDOI
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future.
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Quantum walks: a comprehensive review
TL;DR: This paper has reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.
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Advances in quantum cryptography
Stefano Pirandola,Ulrik L. Andersen,Leonardo Banchi,Mario Berta,Darius Bunandar,Roger Colbeck,Dirk Englund,Tobias Gehring,Cosmo Lupo,Carlo Ottaviani,Jason Pereira,Mohsen Razavi,Jesni Shamsul Shaari,Marco Tomamichel,Vladyslav C. Usenko,Giuseppe Vallone,Paolo Villoresi,Petros Wallden +17 more
TL;DR: This review begins by reviewing protocols of quantum key distribution based on discrete variable systems, and considers aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems.
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Geometric quantum computation using nuclear magnetic resonance
TL;DR: A nuclear magnetic resonance experiment is performed in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate, and suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations.
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