Quantum Computation with Topological Codes: From Qubit to Topological Fault-ToleranceThis 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. |
Contents
| 1 | |
2 Stabilizer Formalism and Its Applications | 24 |
3 Topological Stabilizer Codes | 56 |
4 Topological Quantum Computation with Surface Codes | 86 |
5 Topologically Protected MeasurementBased Quantum Computation | 107 |
Other editions - View all
Quantum Computation with Topological Codes: From Qubit to Topological Fault ... Keisuke Fujii No preview available - 2015 |
Quantum Computation with Topological Codes: From Qubit to Topological Fault ... Keisuke Fujii No preview available - 2015 |
Common terms and phrases
1-chain acting algorithm ancilla applying approximation arbitrary basis boundary braiding calculated called circuit classical Clifford operations cluster CNOT gate concatenated connected consider consisting correlation corresponds cycle decoding defect pair qubit defect region defined described diagram distance distillation dual edge efficiently eigenvalue elements employed encoded equivalent error probability example explained face fault-tolerant follows Fujii given graph ground Hadamard Hamiltonian hence hexagonal implemented input interactions introduce Jones lattice Lett located logical operators magic mapped MBQC measurement outcomes noise Note obtain Pauli operators perform phase Phys physical plaquette polynomial posterior probability preparation primal provides quantum circuit quantum error correction relation respectively shown in Fig Similarly single-qubit space stabilizer codes stabilizer group stabilizer operator step Suppose surface code syndrome teleportation threshold topological quantum topologically protected transformation transversal unitary operator universal quantum computation X operator X-basis