Quantum Computation with Topological Codes: From Qubit to Topological Fault-Tolerance
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
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2 Stabilizer Formalism and Its Applications
3 Topological Stabilizer Codes
4 Topological Quantum Computation with Surface Codes
5 Topologically Protected MeasurementBased Quantum Computation
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3D cluster arXiv arXiv preprint boundary braid group braiding operation chain complex circuit classical Clifford operations CNOT gate code space concatenated correlation surface corresponds cycle decoding defect pair qubit defect region defined dual 1-chain dual defect edge eigenstate eigenvalue encoded equivalent error chain error syndrome fault-tolerant fault-tolerant quantum computation Fujii graph Hadamard operation Hadamard test homology class implemented input Jones polynomial Kitaev lattice Lett level-k logical error probability logical operators logical qubit magic state distillation MBQC measurement outcomes MWPM n-qubit noise obtain Pauli basis phase Phys plaquette operators posterior probability primal and dual primal defect QEC gadget quantum error correction quantum information RBIM shown in Fig single-qubit stabilizer codes stabilizer formalism stabilizer group stabilizer operator surface code syndrome measurements three-qubit threshold value topological quantum computation topological quantum error topologically ordered topologically protected toric code transformation transversal two-qubit gates unitary operator universal quantum computation vertex Z-type