We present a unified approach to quantum error correction, called operator quantum error correction. Our scheme relies on a generalized notion of a noiseless subsystem that is investigated here. By combining the active error correction with this generalized noiseless subsystems method, we arrive at a unified approach which incorporates the known techniques--i.e., the standard error correction m...

We consider the problem of optimally decoding a quantum error correction code — that is to find the optimal recovery procedure given the outcomes of partial “check” measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performan...

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which characterizes the scale-up in the size of the circuit due to encoding. We carry out a detailed seminumerical threshold analysis for concatenated coding using the seven-qubit CSS code in the local and the ‘nonlo...

purpose:the user interface of federated search engines is very important because it can make effective search, retrieval, and user interaction with the system. . identifying the most important indicators of the federated search engine user interface is a solution to enhance the applicability of the search engine interface. the purpose of this study was to examine the role of search, screen, nav...

We investigate how geometric properties translate into functional properties in sparse networks of computing elements. Specifically, we determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence, in an associative memory mode...

We demonstrate the deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal a Bell state fidelity of F = 0.58 ± 0.04, which is above the entanglement threshold of F = 0.5, without any correction for atom loss, and F = 0.71 ± 0.05 after correcting for background collisional losses. The fid...

The paper presents a case study in examining the bias of two particular formalisms: decision trees and linear threshold units. The immediate result is a new hybrid representation, called a perceptron tree, and an associated learning algorithm called the perceptron tree error correction procedure. The longer term result is a model for exploring issues related to understanding representational bi...

Any research or policy analysis exercise in economics must be consistent with the timeseries properties of observed macroeconomic data. This paper discusses in detail the specification of a six-variable vector error-correction forecasting model. We test for cointegration among those variables: the CPI, the implicit price deflator for GDP, real money balances (M1), the federal funds rate, the yi...

This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques — i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method — as special cases, and reli...

In this paper we evaluate the data transmission performance of a generalized multiple-tree-based overlay architecture for peer-to-peer live streaming that employs multipath transmission and forward error correction. We give mathematical models to describe the error recovery in the presence of packet losses. We evaluate the data distribution performance of the overlay, its asymptotic behavior, t...