This thesis is an exposition of a classification of classical reversible gates acting on bits in terms of the reversible transformations they generate, which was recently completed by the author, Scott Aaronson, and Luke Schaeffer. In particular, we present those portions of the classification which were the main contributions of the author. Most importantly, this thesis contains the proof that...

In this note we show that the nth Morava E-cohomology group of a finite spectrum with action of the nth Morava stabilizer group can be recovered from the (n + 1)st Morava Ecohomology group with action of the (n + 1)st Morava stabilizer group.

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results.

We show how, given any set of generators of the stabilizer of a quantum code, an eecient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists of O(nd) operations, and converts k-qubit data (where k = n ? d) into n-qubit codewords.

xiv Chapter 1: Introduction 1 1.1 A Brief History of Quantum Information Science . . . . . . . . . . . . . . 1 1.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Chapter 2: Quantum Stabilizer Codes 9 2.1 The Stabilizer Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Quantum Error-Correction . . . . . . . . . . . . . . . . . . . . . . . ....

atorvastatin calcium, the lipid lowering agent, is taken as a model drug characterized by poor water solubility and bioavailability. in this study an attempt was made for preparation of nanocrystals using high pressure homogenization. a number of stabilizers were included as well as polymers at different concentrations, and the formulations were homogenized for ten cycles at a pressure of 1000 ...

Recently, the field of quantum error-correcting codes has rapidly emerged as an important discipline. As quantum information is extremely sensitive to noise, it seems unlikely that any large scale quantum computation is feasible without quantum error-correction. In

In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the known results on encoding of stabilizer codes. Along the way we also show how Clifford codes can be encoded. We also show that gauge qubits can be exploited to...

In this paper, tuning of power system stabilizer (PSS) and thyristor controlled series capacitor (TCSC) is studied. The analysis of mode controllability is used to select the effective location for TCSC. The performances of TCSC equipped with a proportional-integral-derivative controller (P-I-D controller) and proportional-integral-derivative power system stabilizer (P-I-D PSS) are investigated...