Abstract
Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of Bernstein-Vazirani and Grover. By combining the tools used in these algorithms—quantum fast transforms and amplitude amplification—with a novel (in this context) tool—a solution method for geometrical optimization problems—we derive a general technique for quantum concept learning. We name this technique “Amplified Impatient Learning” and apply it to construct quantum algorithms solving two new problems: Battleship and Majority, more efficiently than is possible classically.
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Acknowledgments
We thank Zeph Landau, Jeff Remmel and Ronald de Wolf for useful discussions. This work has been partially supported by the National Science Foundation (NSF) under grant ECS-0202087, and by the National Security Agency (NSA) and Advanced Research and Development Activity (ARDA) under Army Research Office (ARO) grant number DAAD19-01-1-0520.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hunziker, M., Meyer, D.A., Park, J. et al. The geometry of quantum learning. Quantum Inf Process 9, 321–341 (2010). https://doi.org/10.1007/s11128-009-0129-6
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DOI: https://doi.org/10.1007/s11128-009-0129-6