Introduction to Topological Quantum Computation
Cambridge University Press, 12 באפר׳ 2012
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
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Abelian anyons adiabatic anyonic model anyonic statistics behaviour boundary charge Chern–Simons theories classical configuration Consider continuous deformations corresponds defined described eigenstates eigenvalues elements employ encoded energy gap entanglement entropy equation equivalent example exchange expectation value fermionic modes ﬁeld finite flux fused fusion channel fusion outcomes fusion rules gauge transformation geometric phase given gives rise ground Hamiltonian Hence Hilbert space holonomy honeycomb lattice model integer interactions Ising anyons Jones polynomials Kitaev magnetic field Majorana fermions matrix non-Abelian anyons non-trivial ofthe parameterised parameters path Pauli phase factor physical plaquette possible properties quantum algorithms quantum double quantum double models quantum gates quantum Hall effect quantum information quasiparticles qubits realised Reidemeister move representation rotations shown in Figure Skein relations sources spin statistical evolutions Stopo topological models topological order topological quantum computation topological systems toric code two-dimensional unitary unitary matrix vacuum vector vertex vortices wave function Wilson loop worldlines