Quantum algorithms for testing properties of distributions

Abstract : Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the L_1-norm ? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the L_1-distance between P and Q can be estimated with a constant precision using approximately N^{1/2} queries in the quantum settings, whereas classical computers need \Omega(N) queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity O(N^{1/3}). The classical query complexity of these problems is known to be \Omega(N^{1/2}).
Document type :
Conference papers
Complete list of metadatas

Cited literature [18 references]  Display  Hide  Download

https://hal.inria.fr/inria-00455782
Contributor : Publications Loria <>
Submitted on : Thursday, February 11, 2010 - 11:08:54 AM
Last modification on : Thursday, February 11, 2010 - 11:16:07 AM
Long-term archiving on : Friday, June 18, 2010 - 8:11:45 PM

File

bravyi.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00455782, version 1

Collections

Citation

Sergey Bravyi, Aram W. Harrow, Avinatan Hassidim. Quantum algorithms for testing properties of distributions. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.131-142. ⟨inria-00455782⟩

Share

Metrics

Record views

182

Files downloads

178