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...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Sourav Chakraborty, Eldar Fischer, Arie Matsliah, Ronald de Wolf
• Keywords: Algorithm, CORR 2010, Education, Quantum, Quantum Algorithms