TY  - BOOK
AU  - A. Yu. Kitaev
AU  - Shen, A.H.
AU  - Vyalyi, M.N.
TI  - Classical and quantum computation
T2  - Graduate studies in mathematics
SN  - 9780821832295
AV  - QA267 
PY  - 2002///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  -  Mathematics
N1  - Introduction

Part I- Classical computation
1. Turing machines
2. Boolean circuits
3. The class NP: Reducibility and completeness
4. Probabilistic algorithms and the class BPP
5. The hierarchy of complexity classes

Part II- Quantum computation
6. Definitions and notation
7. Correspondence between classical and quantum computation
8. Bases for quantum circuits
9. Definition of quantum computation. Examples.
10. Quantum probability
11. Physically realizable transformations of density matrices
12. Measuring operators
13. Quantum algorithms for Abelian groups
14. The quantum analogue of NP: the class BQNP
15. Classical and quantum codes

Part III- Solutions
S1. Problems of Section 1
S2. Problems of Section 2
S3. Problems of Section 3
S5. Problems of Section 5
S6. Problems of Section 6
S7. Problems of Section 7
S8. Problems of Section 8
S9. Problems of Section 9
S10. Problems of Section 10
S11. Problems of Section 11
S12. Problems of Section 12
S13. Problems of Section 13
S15. Problems of Section 15
N2  - This book is an introduction to a new rapidly developing theory of quantum computing. It begins with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. The second part of the book provides an exposition of quantum computation theory. It starts with the introduction of general quantum formalism (pure states, density matrices, and superoperators), universal gate sets and approximation theorems. Then the authors study various quantum computation algorithms: Grover's algorithm, Shor's factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes). --- summary provided by publisher
UR  - https://www.ams.org/books/gsm/047/
ER  -