Towards large scale quantum computation

Why quantum compute?......Page 19
Models of quantum computing......Page 21
The circuit model......Page 22
Cluster states......Page 26
Topological quantum computation......Page 27
Quantum computation is possible in principle......Page 30
Overview......Page 38
The adiabatic Kane cnot gate......Page 41
The Kane architecture......Page 42
Adiabatic cnot pulse profiles......Page 44
Intrinsic dephasing and fidelity......Page 51
Conclusion......Page 52
Adiabatic readout pulse profiles......Page 57
Readout performance......Page 58
Conclusion......Page 60
Implementing arbitrary 2-qubit gates......Page 63
Background......Page 64
Terminology and notation......Page 66
Constructing a canonical decomposition......Page 67
Making a canonical decomposition unique......Page 70
Building gates out of physical interactions......Page 71
Conclusion......Page 73
5-qubit QEC on an LNN QC......Page 75
Compound gates......Page 76
5-qubit LNN QEC......Page 77
Simulation of performance......Page 78
Conclusion......Page 83
QEC without measurement......Page 85
Resetting......Page 86
5-qubit QEC without measurement......Page 87
Conclusion......Page 90
Shor's algorithm......Page 93
Shor's algorithm on an LNN QC......Page 101
Decomposing Shor's algorithm......Page 102
Quantum Fourier Transform......Page 105
Modular Addition......Page 107
Controlled swap......Page 110
Complete Circuit......Page 112
Conclusion......Page 114
Shor's algorithm with a limited set of rotation gates......Page 117
Approximate quantum Fourier transform......Page 118
Dependence of output reliability on period of f(k)=mk-5mumod5mu-N......Page 119
Dependence of output usefulness on integer length and rotation gate set......Page 121
Conclusion......Page 125
Constructing arbitrary single-qubit fault-tolerant gates......Page 127
Finding optimal approximations......Page 128
Simple Steane code single-qubit gates......Page 130
The fault-tolerant T-gate......Page 134
Approximations of phase gates......Page 143
Approximations of arbitrary gates......Page 149
Conclusion......Page 151
Concluding remarks......Page 153
Appendix......Page 154
Simple Steane code gates......Page 159