Nondeterministic Quantum Query and Quantum Communication Complexities

Nondeterministic Quantum Query and Communication Complexities

Properties and Application of Nondeterministic Quantum Query Algorithms

Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zeroerror, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already stu...

Quantum Randomness and Nondeterminism

Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nonde-terminism add power? Although reasonable quantum random sources do not add computational power, the discussion of quantum random-ness naturally leads to several deenitions of the complexity of quantum states. Unlike classical string complexity, both deterministic and non...

Characterization of Non-Deterministic Quantum Query and Quantum Communication Complexity

It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the non-deterministic quantum query complexity of f is linearly related to the degree of a “non-deterministic” polynomial for f . We also prove a quantum-classical...

On the Algebraic Characterization of Nondeterministic Quantum Query Complexity

We improve a result on nondeterministic quantum query complexity given by Ronald de Wolf in his 2003 paper by showing that his algebraic characterization holds when the definition of a nondeterministic polynomial is taken to be a polynomial over the real numbers. In addition, we give an alternate proof of the original lower bound that doesn’t use the probabilistic method. Our proof uses element...