Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

Computing prime factors with a Josephson phase qubit quantum processor

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5], however this has yet to be shown using solid state quantum bits (qubits). Two advantages of superconducting qubit architectures are the use of conventional microfabrication techniques, which allow straightforward scaling to large numbers of qubits, and a toolkit of circuit elements that can be used to engineer a variety of qubit types and interactions[6, 7]. Using a number of recent qubit control and hardware advances [7-13], here we demonstrate a nine-quantum-element solid-state QuP and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produces coherent interactions between five qubits and verify bi- and tripartite entanglement via quantum state tomography (QST) [8, 12, 14, 15]. In the final experiment, we run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. Improvements in the superconducting qubit coherence times and more complex circuits should provide the resources necessary to factor larger composite numbers and run more intricate quantum algorithms.Comment: 5 pages, 3 figure

Coverage of multiple recessions using the tunnel technique and a collagen matrix in the maxilla or mandible: a 6-month study

Multiple recession defects in the dentition of the patients are routinely encountered in clinical practice and as such present a challenge for clinicians. Periodontal plastic surgical procedures aim to restore both esthetics as function in periodontal tissues. The objective of this study was to evaluate and compare the clinical efficacy of using a tunnel technique with a collagen matrix to cover multiple recessions in the maxilla or mandible. Fourteen patients were enrolled in the study. Patients in the maxilla-group and mandible-group were treated with xenogeneic collagen matrix using the tunnel technique. Clinical recordings were obtained at baseline and after 3 and 6 months. The percentage of average recession coverage (ARC), the percentage rate of patients with complete coverage of all recessions (CRC-1) and the percentage rate of complete coverage of recession defects (CRC-2) were evaluated after 3 and 6 months after the surgery. Statistically significant differences were observed in every parameter except probing depth between the baseline values compared to the values 3 and 6 months after the procedure in both groups. The mean ARC 6 months after the procedure was 96.8% in the maxilla and 81.3% in the mandible. At 6 months after the procedure, a complete root coverage was obtained in 2 out of 9 patients and 31 out of 39 recessions (79%) in the maxilla and 0 out of 5 patients and 10 out of 20 recessions (50%) in the mandible. A collagen matrix combined with the tunnel technique led to a satisfactory ARC, CRC- 2 and resulted in an unsatisfactory CRC-1

Coverage of multiple recessions using the tunnel technique and a collagen matrix in the maxilla or mandible: A 6 month study

Multiple recession defects in the dentition of the patients are routinely encountered in clinical practice and as such present a challenge for clinicians. Periodontal plastic surgical procedures aim to restore both esthetics as function in periodontal tissues. The objective of this study was to evaluate and compare the clinical efficacy of using a tunnel technique with a collagen matrix to cover multiple recessions in the maxilla or mandible. Fourteen patients were enrolled in the study. Patients in the maxilla-group and mandible-group were treated with xenogeneic collagen matrix using the tunnel technique. Clinical recordings were obtained at baseline and after 3 and 6 months. The percentage of average recession coverage (ARC), the percentage rate of patients with complete coverage of all recessions (CRC-1) and the percentage rate of complete coverage of recession defects (CRC-2) were evaluated after 3 and 6 months after the surgery. Statistically significant differences were observed in every parameter except probing depth between the baseline values compared to the values 3 and 6 months after the procedure in both groups. The mean ARC 6 months after the procedure was 96.8% in the maxilla and 81.3% in the mandible. At 6 months after the procedure, a complete root coverage was obtained in 2 out of 9 patients and 31 out of 39 recessions (79%) in the maxilla and 0 out of 5 patients and 10 out of 20 recessions (50%) in the mandible. A collagen matrix combined with the tunnel technique led to a satisfactory ARC, CRC-2 and resulted in an unsatisfactory CRC-1

Matter wave explorer of gravity (MWXG)

In response to ESA´s Call for proposalsof 5 March 2007 of the COSMIC VISION 2015-2025 plan of the ESA science programme, we propose a M-class satellite mission to test the Equivalence Principle in the quantum domain by investigating the extend free fall of matter waves instead of macroscopic bodies as in the case of GAUGE, MICROSCOPE or STEP. The satellite, called Matter Wave Explorer of Gravity, will carry an experiment to test gravity, namely the measurement of the equal rate of free fall with various isotopes of distinct atomic species with precision cold atom interferometry in the vicinity of the earth. This will allow for a first quantum test of the Equivalence with spin polarized particles and with pure fermionic and bosonic atomic ensembles. Due to teh space conditions, the free fall of Rubidium and Potassium isotopes will be compared with a maximum accelerational sensitivity of 5 x 10^-16 m/s^2 corresponding to an accuracy of the test of the Equivalence Principle of 1 part in 10^16. Besides the primary scientific goal, the quantum test of the Equivalence Principle, the mission can be extended to provide additional information about the gravitational field of the earth or for testing theories of fundamental processes of decoherence which are investigated by various theory groups in the context of quantum gravity phenomenology. In this proposal we present in detail the mission objectives and the technical aspects of the proposed mission