International Symposium on Mathematics, Quantum Theory, and Cryptography

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

International Symposium on Mathematics, Quantum Theory, and Cryptography

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Quantum Circuit Studies with Two-Level Defects of Aluminum Oxide in a Polycrystalline Phase, Amorphous Phase, and at a Metal Surface

This thesis reports on recent achievements toward understanding the nanoscale two-level systems (TLS) within aluminum oxide layers. I will discuss novel experimental and theoretical methods using superconducting resonator data to characterize the TLSs, which are deleterious to qubit coherence. This includes (1) a traditional power dependent loss, which provides the information of collective TLS effects, (2) spectroscopy of individual TLSs by DC-tuning, and (3) two-tone spectroscopy of ensemble TLSs by a second saturation tone. We find that the behaviors of TLSs in different structural phases have distinguishing features. Utilizing the DC-tuning feature of our sensor, we further extract dipole moments from individual TLSs and provide the moment histograms of the two aluminum oxide film types. We observe polycrystalline oxide has an average dipole moment = 2.6 Debye and a single-peak histogram consistent with a single TLS origin. On the other hand, TLSs in amorphous oxide have a wide spread of dipole moment values probably due to oxygen deficiency. Saturation slopes of TLSs in bulk films (polycrystalline and amorphous phases) show a square root dependence of power indicating an ignorable TLS-TLS interaction. Moreover, TLSs in the polycrystalline phase are more stable in the time domain than TLSs in the amorphous phase. Unlike the previous two bulk TLSs, TLSs at the metal-air interface require an explanation from the model assuming TLS frequencies are under stochastic fluctuations originating from TLS-TLS interaction since we find a weak power dependence. We also demonstrate the first published transmon qubits which are solely made from optical lithography. They have a comparable relaxation time and junction resistance to those made from e-beam lithography