A quantitative study of the orientation bias of some edge detector schemes

The evaluation of a particular set of edge detection schemes is described. The results obtained are compared with those obtained from an edge detection scheme using a texture oriented approach. The orientational bias of these schemes is emphasized. Improved qualitative observations are reported and a comparison of the evaluation method with another edge detection evaluation method is presented

Exact quantum query complexity of EXACTk,ln\rm{EXACT}_{k,l}^n

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal algorithm (for some cases), and a nontrivial general lower and upper bound on the minimum number of queries to the black box.Comment: 19 pages, fixed some typos and constraint

Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.Comment: v2: 4 pages, 1 figure. Published versio

Seasonal and site-specific variation in vapour and aerosol phase PAHs over Flanders (Belgium) and their relation with anthropogenic activities

Peer reviewe

Simple Realization Of The Fredkin Gate Using A Series Of Two-body Operators

The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.Comment: Revtex 3.0, 7 pages, 3 figures appended at the end, please refer to the comment lines at the beginning of the manuscript for reasons of replacemen

The Measurement Calculus

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. To appear in Journal of AC

Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$ is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proved that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics.Comment: 37 pages Latexwith 2 postscript figures tar+gzip+uuencoded, to be published in Phys. Rev.

Experimental application of decoherence-free subspaces in a quantum-computing algorithm

For a practical quantum computer to operate, it will be essential to properly manage decoherence. One important technique for doing this is the use of "decoherence-free subspaces" (DFSs), which have recently been demonstrated. Here we present the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces; we observe a reduction of the error rate from 35% to essentially its pre-noise value of 8%.Comment: 11 pages, 4 figures, submitted to PR

Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm

We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which attempts to provide a "scalable" implementation on an expectation-value NMR quantum computer. We show that this ensemble implementation of the DJ algorithm is at best as efficient as the classical random algorithm. As soon as any attempt is made to classify all possible functions with certainty, the implementation requires an exponentially large number of molecules. The discrepancies arise out of the interpretation of mixed state density matrices.Comment: Minor changes, reference added, replaced with publised versio

Quantum Nondemolition Monitoring of Universal Quantum Computers

The halt scheme for quantum Turing machines, originally proposed by Deutsch, is reformulated precisely and is proved to work without spoiling the computation. The ``conflict'' pointed out recently by Myers in the definition of a universal quantum computer is shown to be only apparent. In the context of quantum nondemolition (QND) measurement, it is also shown that the output observable, an observable representing the output of the computation, is a QND observable and that the halt scheme is equivalent to the QND monitoring of the output observable.Comment: 5 pages, RevTeX, no figures, revised, to appear in Phys. Rev. Let