Constructing Quantum Logic Gates Using q-Deformed Harmonic Oscillator Algebras

We study two-level q-deformed angular momentum states and us- ing q-deformed harmonic oscillators, we provide a framework for con- structing qubits and quantum gates. We also present the construction of some basic quantum gates including CNOT, SWAP, Toffoli and Fredkin.Comment: Slightly modified version of the accepted manuscrip

Powering quantum Otto engines only with q-deformation of the working substance

We consider a quantum Otto cycle with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the cycle. In usual quantum Otto cycle, a Hamiltonian parameter is varied during the quantum adiabatic stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a quantum Otto cycle without any classical analog.Comment: 8 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2208.0856

Progress in Group Field Theory and Related Quantum Gravity Formalisms

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research

Theory of Superconducting Phase Qubits

The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Symmetric Minimal Quantum Tomography and Optimal Error Regions

Ph.DDOCTOR OF PHILOSOPH

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