Related papers: Quantum Counting on the Complete Bipartite Graph

Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was…

Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…

Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…

We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the…

The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…

Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…

We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…

We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…

Currently there are three major paradigms of quantum computation, the gate model, annealing, and walks on graphs. The gate model and quantum walks on graphs are universal computation models, while annealing plays within a specific subset of…

Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…

Protein design is a technique to engineer proteins by modifying their sequence to obtain novel functionalities. In this method, amino acids in the sequence are permutated to find the low energy states satisfying the configuration. However,…

We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…

By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…

The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator…

We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain…

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…

We present a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which…