**Proceedings of Symposia in Applied Mathematics**

Volume: 68;
2010;
348 pp;
Hardcover

MSC: Primary 81; 68; 57; 20;

**Print ISBN: 978-0-8218-4828-9
Product Code: PSAPM/68**

List Price: $100.00

AMS Member Price: $80.00

MAA Member Price: $90.00

**Electronic ISBN: 978-0-8218-9284-8
Product Code: PSAPM/68.E**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

# Quantum Information Science and Its Contributions to Mathematics

Share this page *Edited by *
*Samuel J. Lomonaco, Jr.*

This volume is based on lectures delivered at
the 2009 AMS Short Course on Quantum Computation and Quantum
Information, held January 3–4, 2009, in Washington, D.C.

Part I of this volume consists of two papers giving introductory
surveys of many of the important topics in the newly emerging field of
quantum computation and quantum information, i.e., quantum information
science (QIS). The first paper discusses many of the fundamental
concepts in QIS and ends with the curious and counter-intuitive
phenomenon of entanglement concentration. The second gives an
introductory survey of quantum error correction and fault tolerance,
QIS's first line of defense against quantum decoherence.

Part II consists of four papers illustrating how QIS research is
currently contributing to the development of new research directions
in mathematics. The first paper illustrates how differential geometry
can be a fundamental research tool for the development of compilers
for quantum computers. The second paper gives a survey of many of the
connections between quantum topology and quantum computation. The last
two papers give an overview of the new and emerging field of quantum
knot theory, an interdisciplinary research field connecting quantum
computation and knot theory. These two papers illustrate surprising
connections with a number of other fields of mathematics.

In the appendix, an introductory survey article is also provided
for those readers unfamiliar with quantum mechanics.

#### Readership

Graduate students and research mathematicians interested in quantum information theory and its relations to new research areas in mathematics.