Theory of quanputers. (English. Russian original) Zbl 1441.81066
J. Math. Sci., New York 153, No. 2, 159-166 (2008); translation from Sovrem. Mat. Prilozh. 44, 113-121 (2007).
Summary: In this paper, quantum computers are considered as a part of the family of the reversible, linearly-extended, dynamical systems called quanputers. For classical problems an operational reformulation is given. A universal algorithm for solving classical and quantum problems on quanputers is formulated.
References:
| [1] | L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasiliev, Field Theoretic Renormalization Group in Fully Developed Turbulence, Gordon and Breach (1998). · Zbl 0956.76002 |
| [2] | P. Becher and H. Joos, Z. Phys., 15, 343 (1982). |
| [3] | F. Berezin and M. Shubin, Schrödinger Equation, Kluwer, Dordrecht (1991). · Zbl 0749.35001 |
| [4] | G. D. Birkhoff, Dynamical Systems, Amer. Math. Soc., Providence, Rhode Island (1927). · JFM 53.0732.01 |
| [5] | J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill, New York (1965). · Zbl 0184.54201 |
| [6] | Ta-Pei Cheng and Ling-Fong Li, Gauge Theory of Elementary Particle Physics, Clarendon Press, Oxford (1984). |
| [7] | A. Ecert and R. Jozsa, Rev. Mod. Phys., 68, 115 (1996). |
| [8] | L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin (1987). · Zbl 1111.37001 |
| [9] | R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965). · Zbl 0176.54902 |
| [10] | E. Gozzi, Progr. Theor. Phys. Suppl., 111, 115 (1992). · doi:10.1143/PTPS.111.115 |
| [11] | N. M. Makhaldiani, Computational quantum field theory, Commun. JINR, P2-86-849, Dubna (1986). |
| [12] | N. Makhaldiani, How to solve the classical problems on quantum computers, Commun. JINR, E2-2001-137, Dubna (2001). |
| [13] | N. Makhaldiani, Classical and quantum problems for quanputers, quant-ph/0210184. |
| [14] | N. Makhaldiani, New Hamiltonization of the Schrödinger equation by corresponding nonlinear equation for the potential, Commun. JINR, E2-2000-179, Dubna (2000). |
| [15] | N. Makhaldiani and O. Voskresenskaya, On the correspondence between the dynamics with odd and even brackets and generalized Nambu’s mechanics, Commun. JINR, E2-97-418, Dubna (1997). |
| [16] | H. De Raedt and E. Michielsen, Computational methods for simulating quantum computers, quant-ph/0406210. · Zbl 1009.81010 |
| [17] | T. Toffoli and N. Margolus, Cellular Automata Machines, MIT Press (1987). · Zbl 0655.68055 |
| [18] | C. Zalka, Proc. London Roy. Soc., A454, 313 (1998). · Zbl 0915.68048 · doi:10.1098/rspa.1998.0162 |
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