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CORR
2010
Springer

New Results on Quantum Property Testing

9 years 2 months ago
New Results on Quantum Property Testing
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle f : [n] [m]. Here the probability Pf (j) of an outcome j [m] is the fraction of its domain that f maps to j. We give quantum algorithms for testing whether two such distributions are identical or -far in L1-norm. Recently, Bravyi, Hassidim, and Harrow [11] showed that if Pf and Pg are both unknown (i.e., given by oracles f and g), then this testing can be done in roughly m quantum queries to the functions. We consider the case where the second distribution is known, and show that testing can be done with roughly m1/3 quantum queries, which we prove to be essentially optimal. In contrast, it is known that classical testing algorithms need about m2/3 queries in the unknown-unknown case and about m queries in the known-unknown case. Based on this result, we also re...
Sourav Chakraborty, Eldar Fischer, Arie Matsliah,
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Sourav Chakraborty, Eldar Fischer, Arie Matsliah, Ronald de Wolf
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