Measured Quantum Fourier Transform of 1024 Qubits on Fiber Optics

Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful QFT demonstration on 1024 qubits.Comment: 15 pages, 6 figures, submitted to EQIS 2003 Special issue, Int. J. Quantum Informatio

Fast simulation of animal locomotion: Lamprey swimming

© 2006 by International Federation for Information Processing. All rights reserved. Biologically realistic computer simulation of vertebrate locomotion is an interesting and challenging problem with applications in computer graphics and robotics. One current approach simulates a relatively simple vertebrate, the lamprey, using recurrent neural networks for the spine and a physical model for the body. The model is realized as a system of differential equations. The drawback with this approach is the slow speed of simulation. This paper describes two approaches to speeding up simulation of lamprey locomotion without sacrificing too much biological realism: (i) use of superior numerical integration algorithms and (ii) simplifications to the neural architecture of the lamprey

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Effects of imperfections for Shor's factorization algorithm

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength $\epsilon_c$ which drops only polynomially with $\log_2 N$. The numerical dependence of $\epsilon_c$ on $\log_2 N$ is explained by analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits.Comment: 10 pages, 10 figures, 1 table. Added references and new data. Erratum added as appendix. 1 Figure and 1 Table added. Research is available at http://www.quantware.ups-tlse.fr

Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the Quantum Logic Array (QLA) architecture. Our results show that due to the exponential scaling of the computational time with the desired precision of the energy, significant amount of error correciton is required to implement the TIM problem. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.Comment: 19 pages, 8 figure

Implementing Shor's algorithm on Josephson Charge Qubits

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits is available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.Comment: 12 pages, submitted to Phys. Rev.

The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning

An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit. We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.Comment: 29 pages, 28 figs. New in v2: a section presenting in detail our characterization of Bell's theorem as a contradiction arising from (i) the framework of causal models, (ii) the principle of no fine-tuning, and (iii) certain operational features of quantum theory; a section explaining why a denial of hidden variables affords even fewer opportunities for causal explanations of quantum correlation

Early anterior cingulate involvement is seen in presymptomatic MAPT P301L mutation carriers

BACKGROUND: PET imaging of glucose metabolism has revealed presymptomatic abnormalities in genetic FTD but has not been explored in MAPT P301L mutation carriers. This study aimed to explore the patterns of presymptomatic hypometabolism and atrophy in MAPT P301L mutation carriers. METHODS: Eighteen asymptomatic members from five families with a P301L MAPT mutation were recruited to the study, six mutation carriers, and twelve mutation-negative controls. All participants underwent standard behavioural and cognitive assessment as well as [18F]FDG-PET and 3D T1-weighted MRI brain scans. Regional standardised uptake value ratios (SUVR) for the PET scan and volumes calculated from an automated segmentation for the MRI were obtained and compared between the mutation carrier and control groups. RESULTS: The mean (standard deviation) estimated years from symptom onset was 12.5 (3.6) in the mutation carrier group with a range of 7 to 18 years. No differences in cognition were seen between the groups, and all mutation carriers had a global CDR plus NACC FTLD of 0. Significant reduction in [18F] FDG uptake in the anterior cingulate was seen in mutation carriers (mean 1.25 [standard deviation 0.07]) compared to controls (1.36 [0.09]). A similar significant reduction was also seen in grey matter volume in the anterior cingulate in mutation carriers (0.60% [0.06%]) compared to controls (0.68% [0.08%]). No other group differences were seen in other regions. CONCLUSIONS: Anterior cingulate hypometabolism and atrophy are both apparent presymptomatically in a cohort of P301L MAPT mutation carriers. Such a specific marker may prove to be helpful in stratification of presymptomatic mutation carriers in future trials

Neuroanatomical correlates of perceived usability

Usability has a distinct subjective component, yet surprisingly little is known about its neural basis and relation to the neuroanatomy of aesthetics. To begin closing this gap, we conducted two functional magnetic resonance imaging studies in which participants were shown static webpages (in the first study) and videos of interaction with webpages (in the second study). The webpages were controlled so as to exhibit high and low levels of perceived usability and perceived aesthetics. Our results show unique links between perceived usability and brain areas involved in functions such as emotional processing (left fusiform gyrus, superior frontal gyrus), anticipation of physical interaction (precentral gyrus), task intention (anterior cingulate cortex), and linguistic processing (medial and bilateral superior frontal gyri). We use these findings to discuss the brain correlates of perceived usability and the use of fMRI for usability evaluation and for generating new user experiences