BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
Testing permutation properties through subpermutations
Theoretical Computer Science
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
Quantum weakly nondeterministic communication complexity
Theoretical Computer Science
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A language $L$ has a property tester if there exists a probabilistic algorithm that given an input $x$ queries only a small number of bits of $x$ and distinguishes the cases as to whether $x$ is in $L$ and $x$ has large Hamming distance from all $y$ in $L$. We define a similar notion of quantum property testing and show that there exist languages with good quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.