Superpolynomial Speedups Based on Almost Any Quantum Circuit

@inproceedings{Hallgren2008SuperpolynomialSB,
  title={Superpolynomial Speedups Based on Almost Any Quantum Circuit},
  author={Sean Hallgren and A. Harrow},
  booktitle={ICALP},
  year={2008}
}
  • Sean Hallgren, A. Harrow
  • Published in ICALP 2008
  • Physics, Computer Science, Mathematics
  • The first separation between quantum polynomial time and classical bounded-error polynomial time was due to Bernstein and Vazirani in 1993. They first showed a O(1) vs. Omega(n) quantum-classical oracle separation based on the quantum Hadamard transform, and then showed how to amplify this into a n^{O(1)} time quantum algorithm and a n^{Omega(log n)} classical query lower bound. We generalize both aspects of this speedup. We show that a wide class of unitary circuits (which we call dispersing… CONTINUE READING

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