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2 results

  • Preface

  • Alexander M. Dalzell, AWS Center for Quantum Computing, Sam McArdle, AWS Center for Quantum Computing, Mario Berta, RWTH Aachen University, Przemyslaw Bienias, AWS Center for Quantum Computing, Chi-Fang Chen, University of California, Berkeley, András Gilyén, HUN-REN Alfréd Rényi Institute of Mathematics, Connor T. Hann, AWS Center for Quantum Computing, Michael J. Kastoryano, University of Copenhagen, Emil T. Khabiboulline, National Institute of Standards and Technology, Aleksander Kubica, Yale University, Grant Salton, Amazon Quantum Solutions Lab, Samson Wang, Caltech, Fernando G. S. L. Brandão, AWS Center for Quantum Computing
  • Book:
    Quantum Algorithms
    Published online:
    03 May 2025
    Print publication:
    24 April 2025, pp ix-xiv
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  • Summary

    In the Preface, we motivate the book by discussing the history of quantum computing and the development of the field of quantum algorithms over the past several decades. We argue that the present moment calls for adopting an end-to-end lens in how we study quantum algorithms, and we discuss the contents of the book and how to use it.

  • Mastermind with a linear number of queries

  • Anders Martinsson, Pascal Su
  • Journal:
    Combinatorics, Probability and Computing / Volume 33 / Issue 2 / March 2024
    Published online by Cambridge University Press:
    08 November 2023, pp. 143-156
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  • Since the 1960s Mastermind has been studied for the combinatorial and information-theoretical interest the game has to offer. Many results have been discovered starting with Erdős and Rényi determining the optimal number of queries needed for two colours. For $k$ colours and $n$ positions, Chvátal found asymptotically optimal bounds when $k \le n^{1-\varepsilon }$. Following a sequence of gradual improvements for $k\geq n$ colours, the central open question is to resolve the gap between $\Omega (n)$ and $\mathcal{O}(n\log \log n)$ for $k=n$. In this paper, we resolve this gap by presenting the first algorithm for solving $k=n$ Mastermind with a linear number of queries. As a consequence, we are able to determine the query complexity of Mastermind for any parameters $k$ and $n$.