We present an algebraic framework for interacting extended quantum systems to study
complex phenomena characterized by the coexistence and competition of different states of …

A thorough exposition of quantum computing and the underlying concepts of quantum
physics, with explanations of the relevant mathematics and numerous examples. The …

With a focus on universal quantum computing for quantum simulation, and through the
example of lattice gauge theories, we introduce rather general quantum algorithms that can …

This thesis is a study of the construction and representation of typed models of quantum
mechanics for use in quantum computation. We introduce logical and graphical syntax for …

We examine the problem of simulating lattice gauge theories on a universal quantum
computer. The basic strategy of our approach is to transcribe lattice gauge theories in the …

This concise, accessible text provides a thorough introduction to quantum computing-an
exciting emergent field at the interface of the computer, engineering, mathematical and …

The design of quantum many body systems, which have to fulfill an extensive number of
constraints, appears as a formidable challenge within the field of quantum simulation. Lattice …

We present a quantum-classical algorithm to study the dynamics of the two-spatial-site
Schwinger model on IBM's quantum computers. Using rotational symmetries, total charge …

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals
with classical and quantum dualities in a unified fashion explaining the precise connection …

Physical systems, characterized by an ensemble of interacting constituents, can be
represented and studied by different algebras of operators (observables). For example, a …