Quantum-error correction on linear-nearest-neighbor qubit arrays

A quantum circuit implementing 5-qubit quantum-error correction on a linear-nearest-neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations allowing the circuit to achieve the same depth as the current least depth circuit. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

Continuous quantum error correction by cooling

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.

Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

Vector Error-Correction Models in a consumer packaged goods category forecasting decision support system

A framework for developing marketing category management decision support systems (DSS) based upon the Bayesian Vector Autoregressive (BVAR) model is extended. Since the BVAR model is vulnerable to permanent and temporary shifts in purchasing patterns over time, a form that can correct for the shifts and still provide the other advantages of the BVAR is a Bayesian Vector Error-Correction Model (BVECM). We present the mechanics of extending the DSS to move from a BVAR model to the BVECM model for the category management problem. Several additional iterative steps are required in the DSS to allow the decision maker to arrive at the best forecast possible. The revised marketing DSS framework and model fitting procedures are described. Validation is conducted on a sample problem.

Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.

Operator quantum error correction

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 relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of unitarily noiseless subsystems.

Dizziness and unsteadiness following whiplash injury: Characteristic features and relationship with cervical joint position error

Dizziness and/or unsteadiness are common symptoms of chronic whiplash-associated disorders. This study aimed to report the characteristics of these symptoms and determine whether there was any relationship to cervical joint position error. Joint position error, the accuracy to return to the natural head posture following extension and rotation, was measured in 102 subjects with persistent whiplash-associated disorder and 44 control subjects. Whiplash subjects completed a neck pain index and answered questions about the characteristics of dizziness. The results indicated that subjects with whiplash-associated disorders had significantly greater joint position errors than control subjects. Within the whiplash group, those with dizziness had greater joint position errors than those without dizziness following rotation (rotation (R) 4.5degrees (0.3) vs 2.9degrees (0.4); rotation (L) 3.9degrees (0.3) vs 2.8degrees (0.4) respectively) and a higher neck pain index (55.3% (1.4) vs 43.1% (1.8)). Characteristics of the dizziness were consistent for those reported for a cervical cause but no characteristics could predict the magnitude of joint position error. Cervical mechanoreceptor dysfunction is a likely cause of dizziness in whiplash-associated disorder.

Improving precision and reducing bias in biological surveys: estimating false-negative error rates

The use of presence/absence data in wildlife management and biological surveys is widespread. There is a growing interest in quantifying the sources of error associated with these data. We show that false-negative errors (failure to record a species when in fact it is present) can have a significant impact on statistical estimation of habitat models using simulated data. Then we introduce an extension of logistic modeling, the zero-inflated binomial (ZIB) model that permits the estimation of the rate of false-negative errors and the correction of estimates of the probability of occurrence for false-negative errors by using repeated. visits to the same site. Our simulations show that even relatively low rates of false negatives bias statistical estimates of habitat effects. The method with three repeated visits eliminates the bias, but estimates are relatively imprecise. Six repeated visits improve precision of estimates to levels comparable to that achieved with conventional statistics in the absence of false-negative errors In general, when error rates are less than or equal to50% greater efficiency is gained by adding more sites, whereas when error rates are >50% it is better to increase the number of repeated visits. We highlight the flexibility of the method with three case studies, clearly demonstrating the effect of false-negative errors for a range of commonly used survey methods.

Practical scheme for error control using feedback

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.

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.

A metacognitive contextual intervention to enhance error awareness and functional outcome following traumatic brain injury: A single-case experimental design

Very few empirically validated interventions for improving metacognitive skills (i.e., self-awareness and self-regulation) and functional outcomes have been reported. This single-case experimental study presents JM, a 36-year-old man with a very severe traumatic brain injury (TBI) who demonstrated long-term awareness deficits. Treatment at four years post-injury involved a metacognitive contextual intervention based on a conceptualization of neuro-cognitive, psychological, and socio-environmental factors contributing to his awareness deficits. The 16-week intervention targeted error awareness and self-correction in two real life settings: (a) cooking at home: and (b) volunteer work. Outcome measures included behavioral observation of error behavior and standardized awareness measures. Relative to baseline performance in the cooking setting, JM demonstrated a 44% reduction in error frequency and increased self-correction. Although no spontaneous generalization was evident in the volunteer work setting, specific training in this environment led to a 39% decrease in errors. JM later gained paid employment and received brief metacognitive training in his work environment. JM's global self-knowledge of deficits assessed by self-report was unchanged after the program. Overall, the study provides preliminary support for a metacognitive contextual approach to improve error awareness and functional Outcome in real life settings.