Exact Quantum 1-Query Algorithms and Complexity

Deutsch–Jozsa problem (D–J) has exact quantum 1-query complexity (“exact” means no error), but requires super-exponential queries for the optimal classical deterministic decision trees. D–J problem is equivalent to a symmetric partial Boolean function, and in fact, all symmetric partial Boolean functions having exact quantum 1-query complexity have been found out and these functions can be computed by D–J algorithm. A special case is that all symmetric Boolean functions with exact quantum 1-query complexity follow directly and these functions are also all total Boolean functions with exact quantum 1-query complexity obviously. Then there are pending problems concerning partial Boolean functions having exact quantum 1-query complexity and new results have been found, but some problems are still open. In this paper, we review these results regarding exact quantum 1-query complexity and in particular, we also obtain a new result that a partial Boolean function with exact quantum 1-query complexity is constructed and it cannot be computed by D–J algorithm. Further problems are pointed out for future study.

A Study of Update Methods for BoND-Tree Index on Non-ordered Discrete Vector Data

There is an increasing demand from numerous applications such as bioinformatics and cybersecurity to efficiently process various types of queries on datasets in a multidimensional Non-ordered Discrete Data Space (NDDS). An NDDS consists of vectors with values coming from a non-ordered discrete domain for each dimension. The BoND-tree index was recently developed to efficiently process box queries on a large dataset from an NDDS on disk. The original work of the BoND-tree focused on developing the index construction and query algorithms. No work has been reported on exploring efficient and effective up- date strategies for the BoND-tree. In this paper, we study two update methods based on two different strategies for updating the index tree in an NDDS. Our study shows that using the bottom-up update method can provide improved efficiency, comparing to the traditional top-down update method, especially when the number of dimensions for a vector that need to be updated is small. On the other hand, our study also shows that the two update methods have a comparable effectiveness, which indicates that the bottom-up update method is generally more advantageous.

Span program for non-binary functions

Span programs characterize the quantum query complexity of binary functions f:\{0,\ldots,\ell\}^n \to \{0,1\} up to a constant factor. In this paper we generalize the notion of span programs for functions with non-binary input/output alphabets f: [\ell]^n \to [m]. We show that non-binary span program characterizes the quantum query complexity of any such function up to a constant factor. We argue that this non-binary span program is indeed the generalization of its binary counterpart. We also generalize the notion of span programs for a special class of relations. Learning graphs provide another tool for designing quantum query algorithms for binary functions. In this paper, we also generalize this tool for non-binary functions, and as an application of our non-binary span program show that any non-binary learning graph gives an upper bound on the quantum query complexity.

An improved query for the hidden subbroup problem

The Hidden Subgroup Problem (HSP) is at the forefront of problems in quantum algorithms. In this paper, we introduce a new query, the \textit{character} query, generalizing the well-known phase kickback trick that was first used successfully to efficiently solve Deutsch's problem. An equal superposition query with $\vert 0 \rangle$ in the response register is typically used in the ``standard method" of single-query algorithms for the HSP. The proposed character query improves over this query by maximizing the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.

Diabetes and Hypertension Quality Measurement in Four Safety-Net Sites

SummaryBackground: In this new era after the Health Information Technology for Economic and Clinical Health (HITECH) Act of 2009, the literature on lessons learned with electronic health record (EHR) implementation needs to be revisited.Objectives: Our objective was to describe what implementation of a commercially available EHR with built-in quality query algorithms showed us about our care for diabetes and hypertension populations in four safety net clinics, specifically feasibility of data retrieval, measurements over time, quality of data, and how our teams used this data.Methods: A cross-sectional study was conducted from October 2008 to October 2012 in four safety-net clinics located in the Midwest and Western United States. A data warehouse that stores data from across the U.S was utilized for data extraction from patients with diabetes or hypertension diagnoses and at least two office visits per year. Standard quality measures were collected over a period of two to four years. All sites were engaged in a partnership model with the IT staff and a shared learning process to enhance the use of the quality metrics.Results: While use of the algorithms was feasible across sites, challenges occurred when attempting to use the query results for research purposes. There was wide variation of both process and outcome results by individual centers. Composite calculations balanced out the differences seen in the individual measures. Despite using consistent quality definitions, the differences across centers had an impact on numerators and denominators. All sites agreed to a partnership model of EHR implementation, and each center utilized the available resources of the partnership for Center-specific quality initiatives.Conclusions: Utilizing a shared EHR, a Regional Extension Center-like partnership model, and similar quality query algorithms allowed safety-net clinics to benchmark and improve the quality of care across differing patient populations and health care delivery models.Citation: Benkert R, Dennehy P, White J, Hamilton A, Tanner C, Pohl JM. Diabetes and hypertension quality measurement in four safety-net sites: Lessons learned after implementation of the same commercial electronic health record. Appl Clin Inf 2014; 5: 757–772http://dx.doi.org/10.4338/ACI-2014-03-RA-0019