High-fidelity Z-measurement error encoding of optical qubits

We demonstrate a quantum error correction scheme that protects against accidental measurement, using a parity encoding where the logical state of a single qubit is encoded into two physical qubits using a nondeterministic photonic controlled-NOT gate. For the single qubit input states vertical bar 0 >, vertical bar 1 >, vertical bar 0 > +/- vertical bar 1 >, and vertical bar 0 > +/- i vertical bar 1 > our encoder produces the appropriate two-qubit encoded state with an average fidelity of 0.88 +/- 0.03 and the single qubit decoded states have an average fidelity of 0.93 +/- 0.05 with the original state. We are able to decode the two-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 one-qubit decoded states arising from 16 real and imaginary single-qubit superposition inputs have an average fidelity of 0.96 +/- 0.03.

Global non-dynamic refinement of radial orbit error for altimetric earth satellites

The accuracy of altimetrically derived oceanographic and geophysical information is limited by the precision of the radial component of the satellite ephemeris. A non-dynamic technique is proposed as a method of reducing the global radial orbit error of altimetric satellites. This involves the recovery of each coefficient of an analytically derived radial error correction through a refinement of crossover difference residuals. The crossover data is supplemented by absolute height measurements to permit the retrieval of otherwise unobservable geographically correlated and linearly combined parameters. The feasibility of the radial reduction procedure is established upon application to the three day repeat orbit of SEASAT. The concept of arc aggregates is devised as a means of extending the method to incorporate longer durations, such as the 35 day repeat period of ERS-1. A continuous orbit is effectively created by including the radial misclosure between consecutive long arcs as an infallible observation. The arc aggregate procedure is validated using a combination of three successive SEASAT ephemerides. A complete simulation of the 501 revolution per 35 day repeat orbit of ERS-1 is derived and the recovery of the global radial orbit error over the full repeat period is successfully accomplished. The radial reduction is dependent upon the geographical locations of the supplementary direct height data. Investigations into the respective influences of various sites proposed for the tracking of ERS-1 by ground-based transponders are carried out. The potential effectiveness on the radial orbital accuracy of locating future tracking sites in regions of high latitudinal magnitude is demonstrated.

On the Error-Correcting Performance of some Binary and Ternary Linear Codes

In this work, we determine the coset weight spectra of all binary cyclic codes of lengths up to 33, ternary cyclic and negacyclic codes of lengths up to 20 and of some binary linear codes of lengths up to 33 which are distance-optimal, by using some of the algebraic properties of the codes and a computer assisted search. Having these weight spectra the monotony of the function of the undetected error probability after t-error correction P(t)ue (C,p) could be checked with any precision for a linear time. We have used a programm written in Maple to check the monotony of P(t)ue (C,p) for the investigated codes for a finite set of points of p € [0, p/(q-1)] and in this way to determine which of them are not proper.

Improving the Watermarking Process with Usage of Block Error-Correcting Codes

The emergence of digital imaging and of digital networks has made duplication of original artwork easier. Watermarking techniques, also referred to as digital signature, sign images by introducing changes that are imperceptible to the human eye but easily recoverable by a computer program. Usage of error correcting codes is one of the good choices in order to correct possible errors when extracting the signature. In this paper, we present a scheme of error correction based on a combination of Reed-Solomon codes and another optimal linear code as inner code. We have investigated the strength of the noise that this scheme is steady to for a fixed capacity of the image and various lengths of the signature. Finally, we compare our results with other error correcting techniques that are used in watermarking. We have also created a computer program for image watermarking that uses the newly presented scheme for error correction.

Experiments in Detection and Correction of Russian Malapropisms by Means of the WEB

Malapropism is a semantic error that is hardly detectable because it usually retains syntactical links between words in the sentence but replaces one content word by a similar word with quite different meaning. A method of automatic detection of malapropisms is described, based on Web statistics and a specially defined Semantic Compatibility Index (SCI). For correction of the detected errors, special dictionaries and heuristic rules are proposed, which retains only a few highly SCI-ranked correction candidates for the user’s selection. Experiments on Web-assisted detection and correction of Russian malapropisms are reported, demonstrating efficacy of the described method.

Paronyms for Accelerated Correction of Semantic Errors

* Work done under partial support of Mexican Government (CONACyT, SNI), IPN (CGPI, COFAA) and Korean Government (KIPA Professorship for Visiting Faculty Positions). The second author is currently on Sabbatical leave at Chung-Ang University.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

State protection under collective damping and diffusion

In this paper we provide a recipe for state protection in a network of oscillators under collective damping and diffusion. Our strategy is to manipulate the network topology, i.e., the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies, in order to create a relaxation-diffusion-free channel. This protected channel defines a decoherence-free subspace (DFS) for nonzero-temperature reservoirs. Our development also furnishes an alternative approach to build up DFSs that offers two advantages over the conventional method: it enables the derivation of all the network-protected states at once, and also reveals, through the network normal modes, the mechanism behind the emergence of these protected domains.

Teleportation using coupled oscillator states

We analyze the fidelity of teleportation protocols, as a function of resource entanglement, for three kinds of two-mode oscillator states: states with fixed total photon number, number states entangled at a beam splitter, and the two-mode squeezed vacuum state. We define corresponding teleportation protocols for each case including phase noise to model degraded entanglement of each resource.

Quantum control and quantum entanglement

We discuss quantum error correction for errors that occur at random times as described by, a conditional Poisson process. We shoo, how a class of such errors, detected spontaneous emission, can be corrected by continuous closed loop, feedback.

Heterogeneity, saving-investment dynamics and capital mobility in Latin America

The purpose of this paper is to analyze the dynamics of national saving-investment relationship in order to determine the degree of capital mobility in 12 Latin American countries. The analytically relevant correlation is the short-term one, defined as that between changes in saving and investment. Of special interest is the speed at which variables return to the long run equilibrium relationship, which is interpreted as being negatively related to the degree of capital mobility. The long run correlation, in turn, captures the coefficient implied by the solvency constraint. We find that heterogeneity and cross-section dependence completely change the estimation of the long run coefficient. Besides we obtain a more precise short run coefficient estimate compared to the existent estimates in the literature. There is evidence of an intermediate degree of capital mobility, and the coefficients are extremely stable over time.

Flex cars and the alcohol price

We build a model that incorporates the effect of the innovative ""flex"" car, an automobile that is able to run with either gasoline or alcohol, on the dynamics of fuel prices in Brazil. Our model shows that differences regarding fuel prices will now depend on the proportions of alcohol, gasoline and flex cars in the total stock. Conversely, the demand for each type of car will also depend on the expected future prices of alcohol and gasoline (in addition to the car prices). The model reflects our findings that energy prices are tied in the long run and that causality runs stronger from gasoline to alcohol. The estimated error correction parameter is stable, implying that the speed of adjustment towards equilibrium remains unchanged. The latter result is probably due to a still small fraction of flex cars in the total stock (approx. 5%), despite the fact that its sales nearly reached 100% in 2006. (C) 2009 Elsevier B.V. All rights reserved.

Tests for the hysteresis hypothesis in Brazilian industrialized exports: A threshold cointegration analysis

This paper examines the hysteresis hypothesis in the Brazilian industrialized exports using a time series analysis. This hypothesis finds an empirical representation into the nonlinear adjustments of the exported quantity to relative price changes. Thus, the threshold cointegration analysis proposed by Balke and Fomby [Balke, N.S. and Fomby, T.B. Threshold Cointegration. International Economic Review, 1997; 38; 627-645.] was used for estimating models with asymmetric adjustment of the error correction term. Amongst sixteen industrial sectors selected, there was evidence of nonlinearities in the residuals of long-run relationships of supply or demand for exports in nine of them. These nonlinearities represent asymmetric and/or discontinuous responses of exports to different representative measures of real exchange rates, in addition to other components of long-run demand or supply equations. (C) 2007 Elsevier B.V. All rights reserved.