Seminar • Institute for Quantum Computing — New Insights About Quantum Approximate CountingExport this event to calendar

Tuesday, January 28, 2020 — 2:30 PM EST

Scott Aaronson, David J. Bruton Centennial Professor of Computer Science
University of Texas at Austin

Approximate counting — given a black-box function f:[N]->{0,1}, multiplicatively estimate the number of x’s such that f(x)=1 — is one of the most basic problems in quantum algorithms. In 1998, Brassard, Hoyer, Mosca, and Tapp (BHMT) gave a fully quadratic quantum speedup for the problem, while Nayak and Wu showed that this speedup was optimal. 

What else is there to say? In this talk:

  • I’ll describe a new, “simpler” quantum approximate counting algorithm, which achieves the same speedup as BHMT while requiring no Quantum Fourier Transforms, just pure Grover iterations.
  • I’ll describe a new proof that there’s no exponential speedup for quantum approximate counting, even if, in addition to black-box queries to f, the algorithm also gets uniform superpositions |S> over the set all x’s such that f(x)=1, and the ability to reflect about |S>. The proof relies on a novel generalization of the polynomial method to Laurent polynomials (which can have negative exponents).
  • I’ll sketch a new proof, *also* based on Laurent polynomials, that there’s no super-efficient QMA protocol for approximate counting. 

Based on joint work with Patrick Rall (arXiv:1908.10846) as well as Robin Kothari, William Kretschmer, and Justin Thaler (arXiv:1904.08914).

Location 
QNC - Quantum Nano Centre
0101
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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