R. Feynman, `Quantum mechanical computers', Optics News 11 (1985), 11--20.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(2) Every classical computable function can be computed by a small universal set of gates like OR, NOT or NAND . A set of quantum gates S is called universal if any unitary operation can be approximated with an arbitrary accuracy by a quantum circuit involving gates in S; see more in [20, 21, 24, 11]. The corresponding general zero range quantum Hamiltonian (solvable model) is described in the Appendix as a self adjoint extension A # of the orthogonal sum A 0 l 0 restricted to A 0 E a onto proper domain; here is the input space and E is the inner space (dim (E) 2) The ....

R.P. Feynman. Quantum mechanical computers, Optics News 11 (1985), 11--20.

....information theory, computer science, and quantum physics. It holds the key to computers that may run exponentially faster than any known algorithm that runs on conventional computers for certain problems. The field started in the early 1980s with suggestions by Benio# [Ben80] and Feynman [Fey82, Fey86] Feynman observed that certain quantum mechanical e#ects could not be simulated e#ciently on a computer. This observation led to speculation 38 that perhaps computation in general could be done more e#ciently using quantum e#ects. In 1985, Deutsch defined the universal quantum Turing machine ....

R. P. Feynman. Quantum mechanical computers. Foundations of Physics, 16(6):507--531, 1986.

....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 computer to ....

R. P. Feynman, "Quantum mechanical computers," Opt. News, vol. 11, p. 11, 1985.

....is a quantum lattice gas model that can be used to simulate the behaviorof a macroscopic mass density field governed by a parabolic di#usion equation in the long wavelength limit. The quantum computer is comprisedof a large even numberof qubits. Each qubit is a two energy level quantum system [4, 5]. The high energy quantum state is called one and the low energy quantum state is called zero. The quantum algorithm presented in this paper requires the measurement of these binary statesaf#te the applicationof every two qubit quantum gate operation. Theref #ere quantum phase coherence need only ....

Richard P. Feynman. Quantum mechanical computers. Optics News, 11(2):11--20, 1985.

....known which e ectively means that to solve a problem on Benio s computer, we must already know the answer. Furthermore, the model exhibits quantum behavior only during a computational step. Between the steps it returns to a classical state. A somewhat di erent model was developed by Feynman in [5]. His model is based on representing the operation of the computer as a kind of digital circuit. The circuit, along with some extra information to guide the progress of computation, is then systematically converted into representation of a quantum system. In 1985, David Deutsch developed a fully ....

....t is explicitly mentioned. The role of Hamiltonian in Schr odinger s equation (2.10) is to tell, which kind of connections there are between di erent basis states of the computer. As the laws of quantum physics are reversible, also any description of a quantum computer must be reversible in time [5]. Reversibility is ensured by demanding that the Hamiltonian is a Hermitian matrix. This results in the evolution operator in (2.12) being unitary (the operator can be inverted simply by taking a transpose conjugate) When we speak of reversibility, thinking about classical systems, we usually ....

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Richard P. Feynman. Quantum mechanical computers. Optics News, 11:11-20, February 1985.

....to previously identified phase transitions in search difficulty. The conditions underlying this improvement are described. Much of the algorithm is independent of particular problem instances, making it suitable for implementation as a special purpose device. 1 Introduction Quantum computers [1, 2, 7, 8, 10, 17, 9] use quantum parallelism, i.e. the ability to operate simultaneously on a superposition of many classical states, and interference among different computational paths. A measurement on a superposition gives a definite result, with probabilities determined by the amplitudes of the superposition. A ....

Feynman, R. P. (1986), "Quantum Mechanical Computers", Foundations of Physics 16, 507--531.

.... allowed in quantum gates) but we do not allow inversions (e.g. permitted when double wires are used) The following relatively simple reversible (3,3) gates have been proposed in the literature (they are listed in the chronological order) G1 Fredkin gate F0CAAC [9,17] G2 Feynman gate F0CC6A [8] G3 Peres gate 66CC78 [13] G4 Margolus gate CAB8E4 [10] G5, G6, G7, G8, G9 De Vos gates, respectively 714D2B, 8EB2D4, B4C69A D29CA6, ACE2D8 [2 6] EXPERIMENTAL RESULTS We have ran a program constructing all two gate circuits made of identical reversible (3,3) gates: 3,3) circuits, ....

R.Feynman, "Quantum Mechanical Computers, Optics News , Vol. 11, 1985, pp. 11-20.

....Introduction In order to address questions about quantum limits on computation, and the possibility of interpreting microscopic physical processes in informational terms, it would be useful to have a model which acts as a bridge between microscopic physics and computer science. Feynman and others[2, 6, 10] have provided models in which closed, locally interacting microscopic systems described in terms of the quantum formalism perform deterministic computations. Up until now, however, all such models implemented deterministic serial computation, i.e. only one part of the deterministic system is ....

....it activates that element. Using a collection of two state systems (which he called atoms) to represent bits, Feynman made a quantum version of this model. In what follows, we will think of our two state systems as spin 1 2 particles. 5 Feynman s quantum computer In 1985, Richard Feynman[6] presented a model of computation which was quantum mechanically plausible: there seems to be no fundamental reason why a system like the one he described couldn t be built. 3 In his idealization, he managed to arrange for all of the quantum uncertainty in his computation to be concentrated in ....

R. P. Feynman, "Quantum mechanical computers," Opt. News 11 (1985).

....Camblong, this is a subject beyond science fiction . He considers as real practical limitations the characteristic times and lengths in the atomic scale [44] So we should move to nanotechnologies [188] 82] 83] 167] pionered by Shoulders and Feynman 1 [172] 80] or even quantum mechanical [81] or plasma computers [173] as the limit of human possibilities. All these possible technologies would give an improvement of orders of magnitude over present technologies. But combinatorial optimization problems have an exponential growth of possible configurations to be evaluated, so there ....

R.P. Feynman, "Quantum Mechanical Computers", Foundations of Physics 16 (6), pp. 507 (1986).

....circuits, or cellular automata can be used. They are all universal in the sense that they can simulate each other with only a polynomial overhead. However, these models are based on classical physics, whereas physicists believe that the universe is better described by quantum mechanics. Feynman [13, 14] and Benio [4, 5] were the rst who pointed out that quantum physical systems are apparently dicult to simulate on classical computers, suggesting that there may be a gap between computational models based on classical physics and models based on quantum mechanics. Deutsch [10] introduced the ....

R. Feynman, Quantum Mechanical Computers, Foundations of Physics 16, 507, 1986.

....every scientist. Besides, there is an exciting list of references therein. The important technological task in considering quantum computers is to print the bit on as small a material structure as possible in order to diminish the energy dissipation in the copying process. As mentioned by Feynman [99] the present transistor systems dissipate 10 10 kT. He considered bits written, ridiculously as he said, on a single atom. At present we know this is not ridiculous since we already are talking about atomic transistors [15] 28 15 Quantum ways of thinking Quantum physics is probably a ....

R. P. Feynman, "Quantum mechanical computers", Optics News 11, 11, February 1985 -- 15. Conclusions

....is a quantum lattice gas model that can be used to simulate the behavior of a macroscopic mass density field governed by a parabolic di#usion equation in the long wavelength limit. The quantum computer is comprised of a large even number of qubits. Each qubit is a two energy level quantum system [4, 5]. The high energy quantum state is called one and the low energy quantum state is called zero. The quantum algorithm presented in this paper requires the measurement of these binary states after the application of every two qubit quantum gate operation. Therefore, quantum phase coherence need only ....

Richard P. Feynman. Quantum mechanical computers. Optics News, 11(2):11--20, 1985. pages 3

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R. Feynman, `Quantum mechanical computers', Optics News 11 (1985), 11--20.

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R. Feynman, "Quantum Mechanical Computers," Optics News, 11, 1985, pp. 11-20.

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R. Feynman. Quantum mechanical computers. Optic News, 11:11--20, 1985.

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Feynman R., Quantum-mechanical computers, Suc. Phys. Sci., 1986, V.149, Iss.4, 671--688.

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R. Feynman. Quantum mechanical computers. Optics News, 11:11--20, 1985.

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R. Feynman, "Quantum mechanical computers," Optics News, vol. 11, pp. 11--20, 1985.

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R. Feynman, "Quantum Mechanical Computers," Optics News, 11, 1985, pp. 11-20.

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R. Feynman. Quantum mechanical computers. Found. Phys., 16 (1986), 507--531.

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Feynman R P, Quantum mechanical computers, In Found. of Phys. 16 507-531, 1986.

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R.P. Feynman. Quantum Mechanical Computers. Optics News 11, 11-20 (1985). 19

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Richard P. Feynman. Quantum mechanical computers. Optics News, 11(2):11--20, 1985.

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R. P. Feynman. Quantum mechanical computers. Foundations of Physics, 16(6):507-531, 1986.

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Feynman, R. P., "Quantum Mechanical Computers," Opt. News 11, 11--20 (1985).

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