Mathematics of quantum computation and quantum technology

Preface . . v

Quantum Computation . . 1
1 Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit . . 3
2 A Realization Scheme for Quantum Multi-Object Search . . 47
3 On Interpolating between Quantum and Classical Complexity Classes . . 67
4 Quantum Algorithms for Hamiltonian Simulation . . 89

Quantum Technology . . 113
5 New Mathematical Tools for Quantum Technology . . 115
6 The Probabilistic Nature of Quantum Mechanics . . 149
7 Superconducting Quantum Computing Devices . . 171
8 Nondeterministic Logic Gates in Optical Quantum Computing . . 223

Quantum Information . . 257
9 Exploiting Entanglement in Quantum Cryptographic Probes . . 259
10 Nonbinary Stabilizer Codes . . 287
11 Accessible information about quantum states: An open optimization problem . . 309
12 Quantum Entanglement: Concepts and Criteria . . 349
13 Parametrizations of Positive Matrices With Applications . . 387

Quantum Topology, Categorical Algebra, and Logic . . 407
14 Quantum Computing and Quantum Topology . . 409
15 Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics . . 515
16 Quantum measurements without sums . . 559

Appendix Panel Report on the Forward Looking Discussion . . 597
Index . . 603