Classical and Quantum Computation

Introduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index.

[1]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[2]  A. Steane Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  Andrew Chi-Chih Yao,et al.  Quantum Circuit Complexity , 1993, FOCS.

[4]  Leonard M. Adleman,et al.  Quantum Computability , 1997, SIAM J. Comput..

[5]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6]  A. Kirillov Elements of the theory of representations , 1976 .

[7]  Peter W. Shor,et al.  Algorithms for Quantum Computation: Discrete Log and Factoring (Extended Abstract) , 1994, FOCS 1994.

[8]  Mukarram Ahmad,et al.  Continued fractions , 2019, Quadratic Number Theory.

[9]  Selmer Bringsjord,et al.  P=np , 2004, ArXiv.

[10]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[11]  Richard Cleve,et al.  Fast parallel circuits for the quantum Fourier transform , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[12]  Daniel R. Simon,et al.  On the power of quantum computation , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[13]  László Babai,et al.  Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes , 1988, J. Comput. Syst. Sci..

[14]  Ravi B. Boppana,et al.  The Complexity of Finite Functions , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[15]  D. Coppersmith An approximate Fourier transform useful in quantum factoring , 2002, quant-ph/0201067.

[16]  M. Marcus,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[17]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[18]  J. Frank Adams,et al.  Lectures on Lie groups , 1969 .

[19]  David A. Mix Barrington,et al.  Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 , 1986, STOC '86.

[20]  Jr. Hartley Rogers Theory of Recursive Functions and Effective Computability , 1969 .

[21]  John Watrous,et al.  PSPACE has constant-round quantum interactive proof systems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[22]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[23]  Jozef Gruska,et al.  Quantum Computing , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[24]  Adi Shamir,et al.  IP = PSPACE , 1992, JACM.

[25]  V. Prasolov Problems and theorems in linear algebra , 1994 .

[26]  Alexei Y. Kitaev,et al.  Parallelization, amplification, and exponential time simulation of quantum interactive proof systems , 2000, STOC '00.

[27]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[28]  Alfred V. Aho,et al.  Principles of Compiler Design , 1977 .

[29]  I. Shafarevich,et al.  Basic notions of algebra , 1989 .

[30]  Stephen A. Cook,et al.  Log Depth Circuits for Division and Related Problems , 1986, SIAM J. Comput..

[31]  Clemens Lautemann,et al.  BPP and the Polynomial Hierarchy , 1983, Inf. Process. Lett..

[32]  David K. Smith Theory of Linear and Integer Programming , 1987 .

[33]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[34]  Leo F. Boron,et al.  Algorithms and recursive functions , 1970 .

[35]  Christopher Umans,et al.  Pseudo-random generators for all hardnesses , 2002, Proceedings 17th IEEE Annual Conference on Computational Complexity.

[36]  А Е Китаев,et al.  Квантовые вычисления: алгоритмы и исправление ошибок@@@Quantum computations: algorithms and error correction , 1997 .

[37]  J. Spencer Probabilistic Methods in Combinatorics , 1974 .

[38]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[39]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[40]  Richard J. Lipton,et al.  Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract) , 1995, CRYPTO.

[41]  R. Feynman Simulating physics with computers , 1999 .

[42]  Tomoyuki Yamakami,et al.  NQP_{C} = co-C_{=}P , 1998, quant-ph/9812032.

[43]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[44]  P. K. Suetin,et al.  Linear Algebra and Geometry , 1989 .

[45]  Lance Fortnow,et al.  Are There Interactive Protocols for CO-NP Languages? , 1988, Inf. Process. Lett..

[46]  Avi Wigderson,et al.  P = BPP if E requires exponential circuits: derandomizing the XOR lemma , 1997, STOC '97.

[47]  Noam Nisan,et al.  Quantum circuits with mixed states , 1998, STOC '98.

[48]  John Watrous On quantum and classical space-bounded processes with algebraic transition amplitudes , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[49]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[50]  H. S. Allen The Quantum Theory , 1928, Nature.

[51]  W. Fulton,et al.  Lie Algebras and Lie Groups , 2004 .

[52]  I. Vinogradov,et al.  Elements of number theory , 1954 .