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In this article, John Preskill provides his view on the near-term (5-10 years ahead) societal and commercial impact of quantum-computers. Specifically, the author focuses on what he calls Noisy Intermediate-Scale Quantum (NISQ) technology: quantum computers with 50-100 qubits for which noise in quantum gates will limit the size of quantum circuits that can be executed reliably. Such NISQ devices may be able to perform tasks which surpass the capabilities of today’s classical digital computers and will be useful tools for exploring e.g. many-body quantum physics, and may have other useful applications, but, the author states, the 100-qubit quantum computer will not change the world right away and we should regard them as a significant step toward the more powerful quantum technologies of the future.

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In this article, Matthias Möller and Cornelis Vuik of the Institute of Applied Mathematics at Delft University of Technology describe their vision of future developments in scientific computing that would be enabled by the advent of software-programmable quantum computers. In their analysis they assume that quantum computers will form part of a hybrid accelerated computing platform like GPUs and co-processor cards do today. In particular, they address the potential of quantum algorithms to bring major breakthroughs in applied mathematics and its applications. Finally, the authors give several examples that demonstrate the possible impact of quantum-accelerated scientific computing on society.

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In this paper, Ashley Montanaro, gives a broad overview of quantum algorithms, focusing on algorithms with clear applications and rigorous performance bounds, and including recent progress in the field. The paper does not a detailed discussion of how the quantum algorithms mentioned work, but aims to provide structure to the different classes of quantum-algorithms, which were known in November 2015

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