Innovative Quantum Computing Hb: Innovative Quantum Computing

This book presents new and prospective approaches to quantum computing. It introduces the many possibilities to further develop the mathematical methods of quantum computation and its applications to future functioning and operational quantum computers. In this book, various extensions of the qubit concept, starting from obscure qubits, superqubits and other fundamental generalizations, are considered. New gates, known as higher braiding gates, are introduced. These new gates are implemented as an additional stage of computation for topological quantum computations and unconventional computing when computational complexity is affected by its environment. Other generalizations are considered and explained in a widely accessible and easy-to-understand way. Presented in a book for the first time, these new mathematical methods will increase the efficiency and speed of quantum computing.Part of IOP Series in Coherent Sources, Quantum Fundamentals, and Applications.Key features• Provides new mathematical methods for quantum computing• Presents material in a widely accessible way• Contains methods for unconventional computing where there is computational complexity• Provides methods to increase speed and efficiency PRELIMS.pdf Author biographies Steven Duplij Raimund Vogl CH001.pdf Chapter Obscure qubits and membership amplitudes 1.1 Preliminaries 1.2 Membership amplitudes 1.3 Transformations of obscure qubits 1.4 Kronecker obscure qubits 1.5 Obscure-quantum measurement 1.6 Kronecker obscure-quantum gates 1.7 Double entanglement 1.8 Conclusions References CH002.pdf Chapter Higher braid quantum gates 2.1 Yang–Baxter operators 2.1.1 Yang–Baxter maps and braid group 2.1.2 Constant matrix solutions to the Yang–Baxter equation 2.1.3 Partial identity and unitarity 2.1.4 Permutation and parameter-permutation 4-vertex Yang–Baxter maps 2.1.5 Group structure of 4-vertex and 8-vertex matrices 2.1.6 Star 8-vertex and circle 8-vertex Yang–Baxter maps 2.1.7 Triangle invertible 9- and 10-vertex solutions 2.2 Polyadic braid operators and higher braid equations 2.3 Solutions to the ternary braid equations 2.3.1 Constant matrix solutions 2.3.2 Permutation and parameter-permutation 8-vertex solutions 2.3.3 Group structure of the star and circle 8-vertex matrices 2.3.4 Group structure of the star and circle 16-vertex matrices 2.3.5 Pauli matrix presentation of the star and circle 16-vertex constant matrices 2.3.6 Invertible and noninvertible 16-vertex solutions to the ternary braid equations 2.3.7 Higher 2n-vertex constant solutions to n-ary braid equations 2.4 Invertible and noninvertible quantum gates 2.5 Binary braiding quantum gates 2.6 Higher braiding quantum gates 2.7 Entangling braiding gates 2.7.1 Entangling binary braiding gates 2.7.2 Entangling ternary braiding gates References CH003.pdf Chapter Supersymmetry and quantum computing 3.1 Superspaces and supermatrices 3.2 Super Hilbert spaces and operators 3.3 Qubits and superqubits 3.4 Multi-(super)qubit states 3.5 Innovations References CH004.pdf Chapter Duality quantum computing 4.1 Duality computing and polyadic operations 4.2 Higher duality computing 4.3 Duality quantum mode References CH005.pdf Chapter Measurement-based quantum computing References CH006.pdf Chapter Quantum walks 6.1 Discrete quantum walks 6.1.1 Polyander visualization of quantum walks 6.1.2 Methods of final states computation 6.1.3 Generalizations of discrete-time quantum walks References