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.

Gates for the kane quantum computer in the presence of dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is 8.3x10(-5). We also compute the fidelities of Z, X, swap, and controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.

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.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

On the threshold of forgetting: Amnesiac identities and the Brazilian capital

Centuries after Locke asserted the importance of memory to identity, Freudian psychology argued that what was forgotten was of equal importance as to what was remembered. The closing decades of the nineteenth century saw a rising interest in the nature of forgetting, resulting in a reassessment and newfound distrust of the long revered faculty of memory. The relationship between memory and identity was inverted, seeing forgetting also become a means for forging identity. This newfound distrust of memory manifested in the writings of Nietzsche who in 1874 called for society to learn to feel unhistorically and distance itself from the past - in what was essentially tantamount to a cultural forgetting. Following the Nietzschean call, the architecture of Modernism was also compelled by the need to 'overcome' the limits imposed by history. This paper examines notions of identity through the shifting boundaries of remembering and forgetting, with particular reference to the construction of Brazilian identity through the ‘repression’ of history and memory in the design of the Brazilian capital. Designed as a forward-looking modernist utopia, transcending the limits imposed by the country's colonial heritage, the design for Brasilia exploited the anti-historicist agenda of modernism to emancipate the country from cultural and political associations with the Portuguese Empire. This paper examines the relationship between place, memory and forgetting through a discussion of the design for Brasilia.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Recruitment of single human low-threshold motor units with increasing loads at different muscle lengths

We investigated the recruitment behaviour of low threshold motor units in flexor digitorum superficialis by altering two biomechanical constraints: the load against which the muscle worked and the initial muscle length. The load was increased using isotonic (low load), loaded dynamic (intermediate load) and isometric (high load) contractions in two studies. The initial muscle position reflected resting muscle length in series A, and a longer length with digit III fully extended in series B. Intramuscular EMG was recorded from 48 single motor units in 10 experiments on five healthy subjects, 21 units in series A and,27 in series B, while subjects performed ramp up, hold and ramp down contractions. Increasing the load on the muscle decreased the force, displacement and firing rate of single motor units at recruitment at shorter muscle lengths (P < 0.001, dependent t-test). At longer muscle lengths this recruitment pattern was observed between loaded dynamic and isotonic contractions, but not between isometric and loaded dynamic contractions. Thus, the recruitment properties of single motor units in human flexor digitorum superficialis are sensitive to changes in both imposed external loads and the initial length of the muscle. (C) 2003 Elsevier Ltd. All rights reserved.

Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

Estimating correlations from epidemiological data in the presence of measurement error

Analysis of a major multi-site epidemiologic study of heart disease has required estimation of the pairwise correlation of several measurements across sub-populations. Because the measurements from each sub-population were subject to sampling variability, the Pearson product moment estimator of these correlations produces biased estimates. This paper proposes a model that takes into account within and between sub-population variation, provides algorithms for obtaining maximum likelihood estimates of these correlations and discusses several approaches for obtaining interval estimates. (C) 1997 by John Wiley & Sons, Ltd.

Mid-thoracic tenderness: a comparison of pressure pain threshold between spinal regions, in asymptomatic subjects

Palpation for tenderness forms an important part of the manual therapy assessment for musculoskeletal dysfunction, In conjunction with other testing procedures it assists in establishing the clinical diagnosis. Tenderness in the thoracic spine has been reported in the literature as a clinical feature in musculoskeletal conditions where pain and dysfunction are located primarily in the upper quadrant. This study aimed to establish whether pressure pain thresholds (PPTs) of the mid-thoracic region of asymptomatic subjects were naturally lower than those of the cervical and lumbar areas. A within-subject study design was used to examine PPT at four spinal levels C6, T4, T6, and L4 in 50 asymptomatic volunteers. Results showed significant (P < 0.001) regional differences. PPT values increased in a caudal direction. The cervical region had the lowest PPT scores, that is was the most tender. Values increased in the thoracic region and were highest in the lumbar region. This study contributes to the normative data on spinal PPT values and demonstrates that mid-thoracic tenderness relative to the cervical spine is not a normal finding in asymptomatic subjects. (C) 2001 Harcourt Publishers Ltd.

A systematic approach to error isolation in computerized wastewater simulation models

Activated sludge models are used extensively in the study of wastewater treatment processes. While various commercial implementations of these models are available, there are many people who need to code models themselves using the simulation packages available to them, Quality assurance of such models is difficult. While benchmarking problems have been developed and are available, the comparison of simulation data with that of commercial models leads only to the detection, not the isolation of errors. To identify the errors in the code is time-consuming. In this paper, we address the problem by developing a systematic and largely automated approach to the isolation of coding errors. There are three steps: firstly, possible errors are classified according to their place in the model structure and a feature matrix is established for each class of errors. Secondly, an observer is designed to generate residuals, such that each class of errors imposes a subspace, spanned by its feature matrix, on the residuals. Finally. localising the residuals in a subspace isolates coding errors. The algorithm proved capable of rapidly and reliably isolating a variety of single and simultaneous errors in a case study using the ASM 1 activated sludge model. In this paper a newly coded model was verified against a known implementation. The method is also applicable to simultaneous verification of any two independent implementations, hence is useful in commercial model development.