P. A. Benioff, "Quantum mechanical Hamiltonian models of discrete processes that erase their histories: Applications to Turing machines," Int. J. Theoret. Phys., vol. 21, pp. 177--202, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....logical state passes stochastically into one of equiprobable successors, that step can, if properly harnessed, be used to remove bits of entropy from the computer s environment. Models have been constructed, obeying the usual conventions of classical, quantum, and thermodynamic thought experiments [1], 3] 4] 10] 11] 15] 17] 23] showing both the ability in principle to perform logically reversible computations in a thermodynamically reversible fashion (i.e. with arbitrarily little entropy production) and the ability to harness entropy increases due to data randomization within a ....

P. A. Benioff, "Quantum mechanical Hamiltonian models of discrete processes that erase their histories: Applications to Turing machines," Int. J. Theoret. Phys., vol. 21, pp. 177--202, 1982.

....always correct. What s more, he managed to make his computation run at a constant rate. His system consists of two parts: a collection of reversible logic gates, each made up of several interacting spins, and a chain of clock spins which 3 Less physical models were proposed earlier by Benioff[1], who seems to have been the first to raise the question of quantum computation in print. 5 passes next to each gate in turn. Note that we will think of each wire that runs between two gates as being a very simple reversible gate: one that exchanges the values of the spins at its two ends. In ....

P. A. Benioff, "Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: application to Turing machines, " Int. J. Theor. Physics 21 (1982), 177--202.

.... explicitly addressed the theme of fundamental connections between physics and computer science (rather than more incidental ones, such as computer programs for the numerical integration of differential equations) Ideas such as virtually nondissipative computation [19] and quantum computation [5,18] started gaining legitimacy. The links between a number of physicists and computer scientists interested in these themes were tightened by a follow up workshop on Moskito Island (1982) where an early prototype of cellular automata machine was demonstrated by us. Wolfram s 1983 86 sortie into ....

Benioff, Paul, "Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Applications to Turing machines," Int. J. Theor. Phys. 21 (1982), 177--201.

....into one of n equiprobable successors, that step can, if properly harnessed, be used to remove log 2 n bits of entropy from the computer s environment. Models have been constructed, obeying the usual conventions of classical, quantum, and thermodynamic thought experiments [16, 15, 3, 4] [11, 17, 23, 1, 10] showing both the ability in principle to perform logically reversible computations in a thermodynamically reversible fashion (i.e. with arbitrarily little entropy production) and the ability to harness entropy increases due to data randomization within a computer to reduce correspondingly the ....

P.A. Benioff. Quantum mechanical Hamiltonian models of discrete processes that erase their histories: applications to Turing machines. Int'l J. Theoret. Physics, 21:177--202, 1982.

....invariant) The quantum mechanical analog of the xor gate is known as the controlled not or cnot gate. This gate is particularly different from the classical two bit gate, however, in that it has two outputs. This is necessary because all quantum logic gates must be reversible logic gates [FT82, Ben82, Per85] We shall return to the subject of reversible logic later when we discuss functions. The key observation here is the following: Theorem 1.1 : Any multiple qubit logic gate may be composed from cnot and single qubit gates. Proof: See [BBC 95] 2 This is one of the most striking ....

Paul A. Benioff. Quantum mechanical hamiltonian models of discrete processes that erase their own histories: Application to Turing machines. Int. J. of Theor. Physics, 21(3/4):177, 1982.

....into one of n equiprobable successors, that step can, if properly harnessed, be used to remove log 2 n bits of entropy from the computer s environment. Models have been constructed, obeying the usual conventions of classical, quantum, and thermodynamic thought experiments [16, 15, 3, 4] [11, 17, 23, 1, 10] showing both the ability in principle to perform logically reversible computations in a thermodynamically reversible fashion (i.e. with arbitrarily little entropy production) and the ability to harness entropy increases due to data randomization within a computer to reduce correspondingly the ....

P.A. Benioff. Quantum mechanical Hamiltonian models of discrete processes that erase their histories: applications to Turing machines. Int'l J. Theoret. Physics, 21:177--202, 1982.

.... of records in [14] and Brownian computers [12] for Turing machines and Brownian enzymatic computers [3, 4, 6] with respect to reversible Boolean circuits by [9] for molecular (billiard ball) computers by [21] Brownian computing using Josephson devices in [16] quantum mechanic computers in [1, 2, 17] and notably by R. Feynman [7, 8] All these models seem mutually simulatable. For background information, see [5] In the last three decades there have been many partial precursors and isolated results to the complete mathematical theory developed in this paper. However, it is the formulation of ....

P.A. Benioff. Quantum mechanical Hamiltonian models of discrete processes that erase their histories: applications to Turing machines. Int. J. Theoret. Physics, 21:177--202, 1982.

.... explicitly addressed the theme of fundamental connections between physics and computer science (rather than more incidental ones, such as computer programs for the numerical integration of differential equations) Ideas such as virtually nondissipative computation [19] and quantum computation [5, 18] started gaining legitimacy. The links between a number of physicists and computer scientists interested in these themes were tightened by a follow up workshop on Moskito Island (1982) where an early prototype of cellular automata machine was demonstrated by us. 4 Unbeknownst to those authors, ....

Benioff, Paul, "Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Applications to Turing machines," Int. J. Theor. Phys. 21 (1982), 177--201.

....effects. But, the principles of computation on these devices are still based on classical physics. Until now, several physicists have proposed models of computation based on quantum physics, which are so called quantum computers. In early models of quantum computers such as those of P. A. Benioff [3, 15], researchers placed a great importance on finding a precise representation of Turing machines based on quantum physics. Thus, inherent properties of quantum physics were not involved in those models. In other words, their purpose was to design a good simulator of Turing machines based on quantum ....

P. A. Benioff, "Quantum Mechanical Hamiltonian Models of Discrete Processes That Erase Their Own Histories : Application to Turing Machines", Int. J. Theor. Phys., 21(1982), pp. 177-201.

....computer, this would correspond to the maximum number of operations per second. For a quantum system, the notion of distinct states is well defined: two states are distinct if they are orthogonal. The connection between orthogonality and rate of information processing has previously been discussed[9, 2, 6, 10, 11, 4], but no universal bound was proposed. The minimum time needed for a quantum system to pass from one orthogonal Supported by NSF grant DMS 9596217 and by DARPA contract DABT63 95 C 0130 1 Although many of the computing and communications properies of quantum systems are novel[14, 16, 3] ....

Benioff, P. A., "Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: application to Turing machines," Int. J. Theor. Physics 21 (1982), 177--202.

.... enzymatic computers [3, 4, 6] with respect to reversible Boolean circuits by [9] for molecular (billiard ball) comput 0 0 0 0 1 1 1 1 OUTPUT INPUT 0 0 1 1 0 1 1 0 Figure 3: A billiard ball computer ers by [23] Brownian computing using Josephson devices in [17] quantum mechanic computers in [1, 2, 18] and notably by R. Feynman [7, 8] All these models seem mutually simulatable. For background information, see [5] Implementations in current solid state technologies (nMOS, CMOS, CCD) of two methods of using switches to implement reversible computations are presented in [21] We note that ....

P.A. Benioff. Quantum mechanical Hamiltonian models of discrete processes that erase their histories: applications to Turing machines. Int'l J. Theoret. Physics, 21:177--202, 1982.

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