Quantum search algorithms

TL;DR: This paper has reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.

TL;DR: In this article, the authors review theoretical advances on the foundations of both discrete and continuous-time quantum walks, together with the role that randomness plays in quantum walks and the connections between the mathematical models of coined discrete quantum walk and continuous quantum walks.

TL;DR: The variational quantum eigensolver (or VQE) as mentioned in this paper uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics.

TL;DR: A parallel quantum search algorithm is presented that can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit and improves the time–space trade-off for the element distinctness and collision finding problems.

TL;DR: This book inchides well-known classics such as "On the Criteria to be used in Decomposing Systems into Modules," "On a 'Buzzword': Hierarchical Structure," and "Software Aging."

TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.

TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.

TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems.