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These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…

Quantum Physics · Physics 2007-05-23 Peter W. Shor

Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen…

Quantum Physics · Physics 2023-03-07 He-Liang Huang , Xiao-Yue Xu , Chu Guo , Guojing Tian , Shi-Jie Wei , Xiaoming Sun , Wan-Su Bao , Gui-Lu Long

Quantum computers use quantum mechanical phenomena to perform conventionally intractable calculations for specific problems. Despite being universal machines, quantum computers are not expected to replace classical computers, but rather, to…

Emerging Technologies · Computer Science 2025-07-08 Philip Döbler , Manpreet Singh Jattana

Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…

Quantum Physics · Physics 2025-09-26 R. Au-Yeung , B. Camino , O. Rathore , V. Kendon

Quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. To realize this promise, new capabilities need software solutions that are able to effectively harness…

Quantum Physics · Physics 2025-01-16 Otso Kinanen , Andrés D. Muñoz-Moller , Vlad Stirbu , Tommi Mikkonen

Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…

General Physics · Physics 2020-06-03 Y. I. Ozhigov

Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is…

Emerging Technologies · Computer Science 2021-09-23 Sukhpal Singh Gill , Adarsh Kumar , Harvinder Singh , Manmeet Singh , Kamalpreet Kaur , Muhammad Usman , Rajkumar Buyya

Quantum computing technologies have become a hot topic in academia and industry receiving much attention and financial support from all sides. Building a quantum computer that can be used practically is in itself an outstanding challenge…

Computational Engineering, Finance, and Science · Computer Science 2018-02-16 Matthias Möller , Cornelis Vuik

Quantum computing has quickly emerged as a revolutionary paradigm that holds the potential for greatly enhanced computational capability and algorithmic efficiency, in a wide range of areas. Among the various hardware platforms, neutral…

Quantum Physics · Physics 2026-03-19 Matteo Grotti , Sara Marzella , Gabriella Bettonte , Daniele Ottaviani , Elisa Ercolessi

Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…

Quantum Physics · Physics 2019-10-14 Joschka Roffe

As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of…

Programming Languages · Computer Science 2021-07-15 Kesha Hietala , Robert Rand , Shih-Han Hung , Liyi Li , Michael Hicks

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…

Quantum Physics · Physics 2010-01-19 Andrew M. Childs , Wim van Dam

Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world…

Quantum Physics · Physics 2021-09-29 Ahmed Shokry , Moustafa Youssef

Many researchers have studied the behaviour of successful developers while debugging desktop software. In this paper, we investigate the embedded-software debugging by intermediate programmers through an exploratory study. The bugs are…

Software Engineering · Computer Science 2017-04-12 Pansy Arafa , Daniel Solomon , Samaneh Navabpour , Sebastian Fischmeister

It is expected that quantum computers would enable solving various problems that are beyond the capabilities of the most powerful current supercomputers, which are based on classical technologies. In the last three decades, advances in…

Quantum Physics · Physics 2022-04-01 A. K. Fedorov , N. Gisin , S. M. Beloussov , A. I. Lvovsky

Quantum computing promises to help humanity solve problems that would otherwise be intractable on classical computers. Unlike today's machines, quantum computers use a novel computing process that leverages the foundational quantum…

Physics and Society · Physics 2024-03-06 Matthias Troyer , Emily Violi Benjamin , Ani Gevorkian

This paper describes the verification of the classical software and hardware stack that is used to control cold atom- and superconducting-based quantum computing hardware. The paper serves both as an introduction to quantum computing and to…

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…

Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…

Quantum Physics · Physics 2023-01-18 Thomas Grurl , Christoph Pichler , Jürgen Fuß , Robert Wille

Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…

Quantum Physics · Physics 2026-02-20 Kean Chen , Yuhao Liu , Wang Fang , Jennifer Paykin , Xin-Chuan Wu , Albert Schmitz , Steve Zdancewic , Gushu Li