Quantum Computation with Topological Codes - Info and Reading Options

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Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction to Quantum Computation -- 1.1 Quantum Bit and Elementary Operations -- 1.2 The Solovay--Kitaev Algorithm -- 1.3 Multi-Qubit Gates -- 1.4 Universal Quantum Computation -- 1.5 Quantum Algorithms -- 1.5.1 Indirect Measurement and the Hadamard Test -- 1.5.2 Phase Estimation, Quantum Fourier Transformation, and Factorization -- 1.5.3 A Quantum Algorithm to Approximate Jones Polynomial -- 1.6 Quantum Noise -- 1.7 Summary and Discussion -- 2 Stabilizer Formalism and Its Applications -- 2.1 Stabilizer Formalism -- 2.2 Clifford Operations -- 2.3 Pauli Basis Measurements -- 2.4 Gottesman--Knill Theorem -- 2.5 Graph States -- 2.6 Measurement-Based Quantum Computation -- 2.7 Quantum Error Correction Codes -- 2.8 Magic State Distillation -- 2.8.1 Knill-Laflamme-Zurek Protocol -- 2.8.2 Bravyi-Kitaev Protocol -- 2.9 Summary and Discussion -- 3 Topological Stabilizer Codes -- 3.1 Z2 Chain Complex -- 3.2 A Bit-Flip Code: Exercise -- 3.3 Definition of Surface Codes -- 3.3.1 Surface Code on a Torus: Toric Code -- 3.3.2 Planar Surface Code -- 3.4 Topological Quantum Error Correction -- 3.5 Error Correction and Spin Glass Model -- 3.6 Other Topological Codes -- 3.7 Connection to Topological Order in Condensed Matter Physics -- 3.8 Summary and Discussion -- 4 Topological Quantum Computation with Surface Codes -- 4.1 Defect Pair Qubits -- 4.2 Defect Creation, Annihilation, and Movement -- 4.3 Logical Controlled-NOT Gate by Braiding -- 4.4 Magic State Injections and Distillation -- 4.5 Topological Calculus -- 4.6 Faulty Syndrome Measurements and Noise Thresholds -- 4.7 Summary and Discussion -- 5 Topologically Protected Measurement-Based Quantum Computation -- 5.1 Topological Cluster State in Three Dimensions -- 5.2 Vacuum, Defect, and Singular Qubit Regions

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