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.

Dramatic extension of tumor latency and correction of neurobehavioral phenotype in Atm-mutant mice with a nitroxide antioxidant

Mutations in the ATM gene (mutated in ataxia telangiectasia) in both humans and mice predispose to lymphoid tumors. A defect in this gene also causes neurodegeneration in humans and a less severe neurological phenotype in mice. There is some evidence that oxidative stress contributes to these defects, suggesting that antioxidants could alleviate the phenotype. We demonstrate here that the antioxidant 5-carboxy-1,1,3,3-tetramethylisoindolin-2-yloxyl (CTMIO) dramatically delays the onset of thymic lymphomas in Atm(-/-) mice which is not due to an enhancement of apoptosis by CTMIO. We also show that this compound corrects neurobehavioral deficits in these mice and reduces oxidative damage to Purkinje cells. The likely mechanism of action of CTMIO is due to a reduction in oxidative stress, which is protective against both the tumor progression and the development of neurological abnormalities. These data suggest that antioxidant therapy has considerable potential in the management of ataxia telangiectasia and possibly other neurodegenerative disorders where oxidative stress is implicated. (c) 2006 Elsevier Inc. All rights reserved.

Diagnosis and Correction of Nutritional Disorders in Ginger

This booklet contains descriptions and photographs of symptoms of deficiencies and toxicities of nutrients, including nitrogen, phosphorus, potassium, calcium, magnesium, sulfur, iron, boron, manganese, zinc, copper and molybdenum, and advice on treatment of affected crops.

Development of a questionnaire to assess the relative subjective benefits of presbyopia correction

Purpose To develop a standardized questionnaire of near visual function and satisfaction to complement visual function evaluations of presbyopic corrections. Setting Eye Clinic, School of Life and Health Sciences, Aston University, Midland Eye Institute and Solihull Hospital, Birmingham, United Kingdom. Design Questionnaire development. Methods A preliminary 26-item questionnaire of previously used near visual function items was completed by patients with monofocal intraocular lenses (IOLs), multifocal IOLs, accommodating IOLs, multifocal contact lenses, or varifocal spectacles. Rasch analysis was used for item reduction, after which internal and test–retest reliabilities were determined. Construct validity was determined by correlating the resulting Near Activity Visual Questionnaire (NAVQ) scores with near visual acuity and critical print size (CPS), which was measured using the Minnesota Low Vision Reading Test chart. Discrimination ability was assessed through receiver-operating characteristic (ROC) curve analysis. Results One hundred fifty patients completed the questionnaire. Item reduction resulted in a 10-item NAVQ with excellent separation (2.92), internal consistency (Cronbach a = 0.95), and test–retest reliability (intraclass correlation coefficient = 0.72). Correlations of questionnaire scores with near visual acuity (r = 0.32) and CPS (r = 0.27) provided evidence of validity, and discrimination ability was excellent (area under ROC curve = 0.91). Conclusion Results show the NAVQ is a reliable, valid instrument that can be incorporated into the evaluation of presbyopic corrections.

A review of the surgical options for the correction of presbyopia

Presbyopia is an age-related eye condition where one of the signs is the reduction in the amplitude of accommodation, resulting in the loss of ability to change the eye's focus from far to near. It is the most common age-related ailments affecting everyone around their mid-40s. Methods for the correction of presbyopia include contact lens and spectacle options but the surgical correction of presbyopia still remains a significant challenge for refractive surgeons. Surgical strategies for dealing with presbyopia may be extraocular (corneal or scleral) or intraocular (removal and replacement of the crystalline lens or some type of treatment on the crystalline lens itself). There are however a number of limitations and considerations that have limited the widespread acceptance of surgical correction of presbyopia. Each surgical strategy presents its own unique set of advantages and disadvantages. For example, lens removal and replacement with an intraocular lens may not be preferable in a young patient with presbyopia without a refractive error. Similarly treatment on the crystalline lens may not be a suitable choice for a patient with early signs of cataract. This article is a review of the options available and those that are in development stages and are likely to be available in the near future for the surgical correction of presbyopia.

Comparison of near visual acuity and reading metrics in presbyopia correction

PURPOSE: To provide a consistent standard for the evaluation of different types of presbyopic correction. SETTING: Eye Clinic, School of Life and Health Sciences, Aston University, Birmingham, United Kingdom. METHODS: Presbyopic corrections examined were accommodating intraocular lenses (IOLs), simultaneous multifocal and monovision contact lenses, and varifocal spectacles. Binocular near visual acuity measured with different optotypes (uppercase letters, lowercase letters, and words) and reading metrics assessed with the Minnesota Near Reading chart (reading acuity, critical print size [CPS], CPS reading speed) were intercorrelated (Pearson product moment correlations) and assessed for concordance (intraclass correlation coefficients [ICC]) and agreement (Bland-Altman analysis) for indication of clinical usefulness. RESULTS: Nineteen accommodating IOL cases, 40 simultaneous contact lens cases, and 38 varifocal spectacle cases were evaluated. Other than CPS reading speed, all near visual acuity and reading metrics correlated well with each other (r>0.70, P<.001). Near visual acuity measured with uppercase letters was highly concordant (ICC, 0.78) and in close agreement with lowercase letters (+/- 0.17 logMAR). Near word acuity agreed well with reading acuity (+/- 0.16 logMAR), which in turn agreed well with near visual acuity measured with uppercase letters 0.16 logMAR). Concordance (ICC, 0.18 to 0.46) and agreement (+/- 0.24 to 0.30 logMAR) of CPS with the other near metrics was moderate. CONCLUSION: Measurement of near visual ability in presbyopia should be standardized to include assessment of near visual acuity with logMAR uppercase-letter optotypes, smallest logMAR print size that maintains maximum reading speed (CPS), and reading speed. J Cataract Refract Surg 2009; 35:1401-1409 (C) 2009 ASCRS and ESCRS

Surgical correction of astigmatism during cataract surgery

High levels of corneal astigmatism are prevalent in a significant proportion of the population. During cataract surgery pre-existing astigmatism can be corrected using single or paired incisions on the steep axis of the cornea, using relaxing incisions or with the use of a toric intraocular lens. This review provides an overview of the conventional methods of astigmatic correction during cataract surgery and in particular, discusses the various types of toric lenses presently available and the techniques used in determining the correct axis for the placement of such lenses. Furthermore, the potential causes of rotation in toric lenses are identified, along with techniques for assessing and quantifying the amount of rotation and subsequent management options for addressing post-operative rotation.