Stable quantum memories with limited measurement

We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher dimensional stabilizer codes with string-like excitations, like the toric code.Comment: 11 Pages, 7 Figure

Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a low-temperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.Comment: 14 Pages, 13 figure

Stroboscopic Generation of Topological Protection

Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with $n$-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.Comment: 5 pages, 2 figures. Published versio

Criteria for developing, assessing and selecting candidate EQ-5D bolt-ons.

PURPOSE: 'Bolt-on' dimensions are additional items added to multi-attribute utility instruments (MAUIs) such as EQ-5D that measure constructs not included in the core descriptive system. The use of bolt-ons has been proposed to improve the content validity and responsiveness of the descriptive system in certain settings and health conditions. EQ-5D bolt-ons serve a particular purpose and thus satisfy a certain set of criteria. The aim of this paper is to propose a set of criteria to guide the development, assessment and selection of candidate bolt-on descriptors. METHODS: Criteria were developed using an iterative approach. First, existing criteria were identified from the literature including those used to guide the development of MAUIs, the COSMIN checklist and reviews of existing bolt-ons. Second, processes used to develop bolt-ons based on qualitative and quantitative approaches were considered. The information from these two stages was formalised into draft development and selection criteria. These were reviewed by the project team and iteratively refined. RESULTS: Overall, 23 criteria for the development, assessment and selection of candidate bolt-ons were formulated. Development criteria focused on issues relating to i) structure, ii) language, and iii) consistency with the existing EQ-5D dimension structure. Assessment and selection criteria focused on face and content validity and classical psychometric indicators. CONCLUSION: The criteria generated can be used to guide the development of bolt-ons across different health areas. They can also be used to assess existing bolt-ons, and inform their inclusion in studies and patient groups where the EQ-5D may lack content validity

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Tailoring of the Tell-us Card communication tool for nurses to increase patient participation using Intervention Mapping

Aims and objectives: To describe the tailoring of the Tell-us Card intervention for enhanced patient participation to the Dutch hospital setting using Intervention Mapping as a systematic approach. Background: Even though patient participation is essential in any patient-to-nurse encounter, care plans often fail to take patients' preferences into account. The Tell-us Card intervention seems promising, but needs to be tailored and tested before implementation in a different setting or on large scale. Design: Description of the Intervention Mapping framework to systematically tailor the Tell-us Card intervention to the Dutch hospital setting. Methods: Intervention Mapping consists of: (i) identification of the problem through needs assessment and determination of fit, based on patients and nurses interviews and focus group interviews; (ii) developing a logic model of change and matrices, based on literature and interviews; (iii) selection of theory-based methods and practical applications; (iv) producing programme components and piloting; (v) planning for adoption, implementation and sustainability; and (vi) preparing for programme evaluation. Results: Knowledge, attitude, outcome expectations, self-efficacy and skills were identified as the main determinants influencing the use of the Tell-us Card. Linking identified determinants and performance objectives with behaviour change techniques from the literature resulted in a well-defined and tailored intervention and evaluation plan. Conclusions: The Tell-us Card intervention was adapted to fit the Dutch hospital setting and prepared for evaluation. The Medical Research Council framework was followed, and the Intervention Mapping approach was used to prepare a pilot study to confirm feasibility and relevant outcomes. Relevance to clinical practice: This article shows how Intervention Mapping is applied within the Medical Research Council framework to adapt the Tell-us Card intervention, which could serve as a guide for the tailoring of similar interventions

Finite temperature quantum simulation of stabilizer Hamiltonians

We present a scheme for robust finite temperature quantum simulation of stabilizer Hamiltonians. The scheme is designed for realization in a physical system consisting of a finite set of neutral atoms trapped in an addressable optical lattice that are controllable via 1- and 2-body operations together with dissipative 1-body operations such as optical pumping. We show that these minimal physical constraints suffice for design of a quantum simulation scheme for any stabilizer Hamiltonian at either finite or zero temperature. We demonstrate the approach with application to the abelian and non-abelian toric codes.Comment: 13 pages, 2 figure