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Contents
1 Information is physical, so is computation 1
2 Hilbert space quantum mechanics 2
3 Quantum information theory 5
3.1 Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Reading the book of Nature—a short glance at the prediction catalog . . . . . . . 6
4 Quantum recursion theory 6
4.1 Reversible computation and deletion of (q)bits . . . . . . . . . . . . . . . . . . . . 6
4.2 Selected features of quantum computation . . . . . . . . . . . . . . . . . . . . . . . 6
4.2.1 Copying of quantum bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2.2 Context dependence of qbits . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.3 Universal quantum computer based on the U(2)-gate . . . . . . . . . . . . . . . . . 9
4.4 Other models of universal quantum computation . . . . . . . . . . . . . . . . . . . 10
4.5 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.6 Diagonalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.6.1 Classical case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.6.2 Quantum mechanical case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.6.3 Proper quantum diagonalization . . . . . . . . . . . . . . . . . . . . . . . . 12
5 Quantum algorithmic information 13
6 Quantum omega 14
Appendix 16
A Two-state system 16
B From single to multiple quanta — “second” field quantization 17
C Quantum interference 19
D Universal 2-port quantum gate 21
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