Quantum Versions of Classical Randomized Algorithms

Purifying Quantum States: Quantum and Classical Algorithms

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Isomorphism and Factorization- Classical and Quantum Algorithms

Classical and Quantum Algorithms for Exponential Congruences

Abstract. We discuss classical and quantum algorithms for solvability testing and finding integer solutions x, y of equations of the form af + bg = c over finite fields Fq. A quantum algorithm with time complexity q(log q) is presented. While still superpolynomial in log q, this quantum algorithm is significantly faster than the best known classical algorithm, which has time complexity q(log q)...

Classical and Quantum Algorithms for USO Recognition

Unique Sink Orientations (USOs) are orientations of the hypercube graph capable of encoding many optimization problems, such as linear programming. When a USO is given in implicit form as an oracle, the USO recognition problem aims to distinguish USO from non-USO oracles. In this thesis we introduce a new type of orientation, the pseudo-USOs, which are closely related to the USO recognition pro...

Classical Simulation of Quantum Adiabatic Algorithms Using Mathematica on GPUs

which is connected to C++ code in order to make our platform capable of communicating with a Graphics Processing Unit. We introduce the reader to the behavior of our proposal by simulating a quantum adiabatic algorithm designed for solving hard instances of the 3-SAT problem. We show that our simulator is capable of significantly increasing the number of qubits that can be simulated using class...