Mathematics (Faculty of)
http://hdl.handle.net/10012/9924
Wed, 18 Sep 2019 18:17:56 GMT2019-09-18T18:17:56ZA walk through quantum noise: a study of error signatures and characterization methods
http://hdl.handle.net/10012/15057
A walk through quantum noise: a study of error signatures and characterization methods
Carignan-Dugas, Arnaud
The construction of large scale quantum computing devices might be one of the most exciting
and promising endeavors of the 21st century, but it also comes with many challenges.
As quantum computers are supplemented with more registers, their error profile generally
grows in complexity, rendering the enterprise of quantifying the reliability of quantum computations
increasingly difficult through naive characterization techniques. In the last decade,
a lot of efforts has been directed toward developing highly scalable benchmarking schemes.
A leading family of characterization methods built upon scalable principles is known as randomized
benchmarking (RB).
In this thesis, many tools are presented with the objective of improving the scalability,
and versatility of RB techniques, as well as demonstrating their reliability under various
error models.
The first part of this work investigates the connection between the error of individual
circuit components and the error of their composition. Before reasoning about intricate circuit
constructions, it is shown that there exists a well-motivated way to define decoherent
quantum channels, and that every channel can be factorized into a unitary-decoherent composition.
This dichotomy carries to the circuit evolution of important error parameters by
assuming realistic error scenarios. Those results are used to improve the confidence interval
of RB diagnoses and to reconcile experimentally estimated parameters with physically and
operationally meaningful quantities.
In the second part of this thesis, various RB schemes are either developed or more rigorously
analyzed. A first result consists of the introduction of “dihedral benchmarking”, a
technique which, if performed in conjunction with standard RB protocols, enables the characterization
of operations that form a universal gate-set. Finally, rigorous analysis tools are
provided to demonstrate the reliability of a highly scalable family of generator-based RB
protocols known as direct RB.
Tue, 17 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10012/150572019-09-17T00:00:00ZDomain Ordering and Box Cover Problems for Beyond Worst-Case Join Processing
http://hdl.handle.net/10012/15053
Domain Ordering and Box Cover Problems for Beyond Worst-Case Join Processing
Alway, Kaleb
Join queries are a fundamental computational task in relational database management systems. For decades, complex joins were most often computed by decomposing the query into a query plan made of a sequence of binary joins. However, for cyclic queries, this type of query plan is sub-optimal. The worst-case run time of any such query plan exceeds the number of output tuples for any query instance.
Recent theoretical developments in join query processing have led to join algorithms which are worst-case optimal, meaning that they run in time proportional to the worst-case output size for any query with the same shape and the same number of input tuples. Building on these results are a class of algorithms providing bounds which go beyond
this worst-case output size by exploiting the structure of the input instance rather than just the query shape.
One such algorithm, Tetris, is worst-case optimal and also provides an upper bound on its run time which depends on the minimum size of a geometric box certificate for the input query. A box certificate is a subset of a box cover whose union covers every tuple which is not present in the query output. A box cover is a set of n-dimensional boxes which cover all of the tuples not contained in the input relations. Many query instances admit different box certificates and box covers when the values in the attributes' domains are ordered differently. If we permute the input query according to a domain ordering which admits a smaller box certificate, use the permuted query as input to Tetris, then transform the result back with the inverse domain ordering,
we can compute the query faster than was possible if the domain ordering was fixed. If we can efficiently compute an optimal domain ordering for a query, then we can state a beyond worst-case bound that is stronger than what is provided by Tetris.
This paper defines several optimization problems over the space of domain orderings where the objective is to minimize the size of either the minimum box certificate or the minimum box cover for the given input query. We show that most of these problems are NP-hard. We also provide approximation algorithms for several of these problems.
The most general version of the box cover minimization problem we will study, BoxMinPDomF, is shown to be NP-hard, but we can compute an approximation only a poly-logarithmic factor larger than K^(a*r), where K is the minimum box cover size under any domain ordering and r is the maximum number of attributes in a relation. This result allows us to compute join queries in time N+K^(a*r*(w+1))+Z, times a poly-logarithmic factor in N, where N is the number of input tuples, w is the treewidth of the query, and Z is the number of output tuples. This is a new beyond worst-case bound. There are queries for which this bound is exponentially smaller than any bound provided by Tetris.
The most general version of the box certificate minimization problem we study, CertMinPDomF, is also shown to be NP-hard. It can be computed exactly if the minimum box certificate size is at most 3, but no approximation algorithm for an arbitrary minimum size is known. Finding such an approximation algorithm is an important direction for future research.
Tue, 17 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10012/150532019-09-17T00:00:00ZA+ Indexes: Highly Flexible Adjacency Lists in Graph Database Management Systems
http://hdl.handle.net/10012/15051
A+ Indexes: Highly Flexible Adjacency Lists in Graph Database Management Systems
Khaliq, Shahid
Adjacency lists are the most fundamental storage structure in existing graph database management systems (GDBMSs) to index input graphs. Adjacency lists are universally linked-list like per-vertex structures that allow access to a set of edges that are all adjacent to a vertex. In several systems, adjacency lists can also allow efficient access to subsets of a vertex’s adjacent edges that satisfy a fixed set of predicates, such as those that have the same label, and support a fixed set of ordering criteria, such as sorting by the ID of destination vertices of the edges. This thesis describes a highly-flexible indexing subsystem for GDBMSs, which consists of two components. The primary component called A+ indexes store adjacency lists, which compared to existing adjacency lists, provide flexibility to users in three aspects: (1) in addition to per-vertex adjacency lists, users can define per-edge adjacency lists; (2) users can define adjacency lists for sets of edges that satisfy a wide range of predicates; and (3) provide flexible sorting criteria. Indexes in existing GDBMS, such as adjacency list, B+ tree, or hash indexes, index as elements the vertices or edges in the input graph. The second component of our indexing sub-system is secondary B+ tree and bitmap indexes that index aggregate properties of adjacency lists in A+ indexes. Therefore, our secondary indexes effectively index adjacency lists as elements. We have implemented our indexing sub-system on top of the Graphflow GDBMS. We describe our indexes, the modifications we had to do to Graphflow’s optimizer, and our implementation. We provide extensive experiments demonstrating both the flexibility and efficiency of our indexes on a large suite of queries from several application domains.
Tue, 17 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10012/150512019-09-17T00:00:00ZProcedurally Rhetorical Verb-Centric Frame Semantics as a Knowledge Representation for Argumentation Analysis of Biochemistry Articles
http://hdl.handle.net/10012/15021
Procedurally Rhetorical Verb-Centric Frame Semantics as a Knowledge Representation for Argumentation Analysis of Biochemistry Articles
Alliheedi, Mohammed
The central focus of this thesis is rhetorical moves in biochemistry
articles. Kanoksilapatham has provided a descriptive theory of
rhetorical moves that extends Swales' CARS model to the complete
biochemistry article. The thesis begins the construction of a computational
model of this descriptive theory. Attention is placed on the Methods
section of the articles. We hypothesize that because authors' argumentation
closely follows their experimental procedure, procedural verbs may
be the guide to understanding the rhetorical moves. Our work proposes
an extension to the normal (i.e., VerbNet) semantic roles especially
tuned to this domain. A major contribution is a corpus of Method sections
that have been marked up for rhetorical moves and semantic roles.
The writing style of this genre tends to occasionally omit semantic
roles, so another important contribution is a prototype ontology
that provides experimental procedure knowledge for the biochemistry
domain. Our computational model employs machine learning to build its
models for the semantic roles and rhetorical moves, validated against
a gold standard reflecting the annotation of these texts by human experts.
We provide significant insights into how to derive these annotations,
and as such have contributions as well to
the general challenge of producing markups in the domain
of biomedical science documents, where specialized knowledge is required.
Thu, 05 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10012/150212019-09-05T00:00:00Z