Contents v
13.1. The problem of hidden subgroup in
(Z2)k;
Simon’s
algorithm 117
13.2. Factoring and finding the period for raising to a power 119
13.3. Reduction of factoring to period finding 120
13.4. Quantum algorithm for finding the period: the basic idea122
13.5. The phase estimation procedure 125
13.6. Discussion of the algorithm 130
13.7. Parallelized version of phase estimation. Applications 131
13.8. The hidden subgroup problem for
Zk
135
14. The quantum analogue of NP: the class BQNP 138
14.1. Modification of classical definitions 138
14.2. Quantum definition by analogy 139
14.3. Complete problems 141
14.4. Local Hamiltonian is BQNP-complete 144
14.5. The place of BQNP among other complexity classes 150
15. Classical and quantum codes 151
15.1. Classical codes 153
15.2. Examples of classical codes 154
15.3. Linear codes 155
15.4. Error models for quantum codes 156
15.5. Definition of quantum error correction 158
15.6. Shor’s code 161
15.7. The Pauli operators and symplectic transformations 163
15.8. Symplectic (stabilizer) codes 167
15.9. Toric code 170
15.10. Error correction for symplectic codes 172
15.11. Anyons (an example based on the toric code) 173
Part 3. Solutions 177
S1. Problems of Section 1 177
S2. Problems of Section 2 183
S3. Problems of Section 3 195
S5. Problems of Section 5 202
S6. Problems of Section 6 203
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