The geometry of quantum learning

  title={The geometry of quantum learning},
  author={Markus Hunziker and David A. Meyer and Ji-Heon Park and James Pommersheim and Mitch Rothstein},
  journal={Quantum Information Processing},
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… 
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A Survey of Quantum Learning Theory
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Guest Column: A Survey of Quantum Learning Theory
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Quantum Counting
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Poly-Locality in Quantum Computing
A class of poly-local transformations, which include the discrete orthogonal wavelet transforms, are described in the hope that these may be helpful in constructing new quantum algorithms.
Quantum algorithms revisited
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Quantum Algorithms for Weighing Matrices and Quadratic Residues
  • W. V. Dam
  • Mathematics, Computer Science
  • 2002
It is shown how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is significantly lower than the classical one, and designed a query problem that uses the Legendre symbol χ.
An exact quantum polynomial-time algorithm for Simon's problem
  • G. Brassard, P. Høyer
  • Computer Science, Mathematics
    Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems
  • 1997
It is shown that there is a decision problem that can be solved in exact quantum polynomial time, which would require expected exponential time on any classical bounded-error probabilistic computer if the data is supplied as a black box.
Efficient Quantum Transforms
A novel network for computing a Fourier transform for a group used in quantum errorcorrection is given and a slightly relaxed definition is shown to simplify the analysis and the networks that computes the transforms.
Reversing quantum dynamics with near-optimal quantum and classical fidelity
We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state’s quantum entanglement or classical correlation with a reference system. We exhibit an approximate
Quantum versus classical learnability
  • R. Servedio, S. Gortler
  • Computer Science
    Proceedings 16th Annual IEEE Conference on Computational Complexity
  • 2001
This work considers quantum versions of two well-studied models of learning Boolean functions: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples to establish a polynomial relationship between the number of quantum versus classical queries required for learning.
Sophisticated quantum search without entanglement
  • Meyer
  • Computer Science, Physics
    Physical review letters
  • 2000
There is a quantum algorithm which searches a "sophisticated" database with a single query, but which it is shown does not require entanglement even for multiparticle implementations.