Related papers: On quantum computation of Kloosterman sums
Starting from a general wave function described on a set of spins/qubits, we propose several quantum algorithms to extract the components of this state on eigenstates of the total spin ${\bf S}^2$ and its azimuthal projection $S_z$. The…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
We propose a new architecture for the measurement-based quantum computation model. The new design relies on small composite light-atom primary clusters. These are then assembled into cluster arrays using ancillary light modes and the actual…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits by using state-of-the-art quantum compressive sensing (CS) methods. In this article, QST…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Measurement-based quantum computation has revolutionized quantum information processing, and the physical systems with which it can be implemented. One simply needs the ability to prepare a particular state, known as the cluster state, and…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics, to general optimization problems.…
A quantum eigensolver is designed under a multi-layer cluster mean-field (CMF) algorithm by partitioning a quantum system into spatially-separated clusters. For each cluster, a reduced Hamiltonian is obtained after a partial average over…
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beamsplitters, phase shifters, single photon…