The geometry of quantum learning

  • Authors:

  • Markus Hunziker;David A. Meyer;Jihun Park;James Pommersheim;Mitch Rothstein

  • Affiliations:

  • Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, USA 92093-0112 and Department of Mathematics, University of Georgia, Athens, USA 30602-740 ...;Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, USA 92093-0112;Department of Mathematics, University of Georgia, Athens, USA 30602-7403 and Department of Mathematics, Pohang University of Science and Technology, Pohang, Kyungbuk, Korea 790-784;Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, USA 92093-0112 and Department of Mathematics, Reed College, Portland, USA 97202-8199;Department of Mathematics, University of Georgia, Athens, USA 30602-7403

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2010

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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.