Related papers: A note on quantum one-way permutations
Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
We consider a problem we call StateIsomorphism: given two quantum states of n qubits, can one be obtained from the other by rearranging the qubit subsystems? Our main goal is to study the complexity of this problem, which is a natural…
Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These…
One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report the first experimental realization of the complete process of deterministic one-way…
Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum computation, communication, and metrology. The realization of quantum networks composed of…
In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
We develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements. We show that the recursive substructure of this representation provides a natural framework for automating the…
We present a novel quantum storage algorithm for k binary vectors of dimension m into a superposition of a m qubit quantum state based on a permutation technique. We compare this algorithm to the storage algorithm proposed by Ventura and…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
A coherent state representation of the expectation value of an arbitrary (but still polynomial) normal ordered quantum operator is discussed. This serves as a basis for developing a fast and easy-to-handle algorithm, based on series of…
We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree-cluster protects the information from transmission loss and enables long-range quantum communication through…
Four-qubit cluster states of two photons entangled in polarization and linear momentum have been used to realize a complete set of single qubit rotations and the C-NOT gate for equatorial qubits with high values of fidelity. By the…
In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done up-front when creating this universal resource, known as a cluster state, on…
We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a…
We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…
Grover's algorithm, a well-know quantum search algorithm, allows one to find the correct item in a database, with quadratic speedup. In this paper we adapt Grover's algorithm to the problem of finding a correct answer to a natural language…