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Oracle quantum computing
 Brassard & U.Vazirani, Strengths and weaknesses of quantum computing
, 1994
"... \Because nature isn't classical, dammit..." ..."
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Cited by 119 (9 self)
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\Because nature isn't classical, dammit..."
CRYSTALLINE COMPUTATION
 CHAPTER 18 OF FEYNMAN AND COMPUTATION (A. HEY, ED.)
, 1999
"... Discrete lattice systems have had a long and productive history in physics. Examples range from exact theoretical models studied in statistical mechanics to approximate numerical treatments of continuum models. There has, however, been relatively little attention paid to exact lattice models which o ..."
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Cited by 36 (8 self)
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Discrete lattice systems have had a long and productive history in physics. Examples range from exact theoretical models studied in statistical mechanics to approximate numerical treatments of continuum models. There has, however, been relatively little attention paid to exact lattice models which obey an invertible dynamics: from any state of the dynamical system you can infer the previous state. This kind of microscopic reversibility is an important property of all microscopic physical dynamics. Invertible lattice systems become even more physically realistic if we impose locality of interaction and exact conservation laws. In fact, some invertible and momentum conserving lattice dynamics—in which discrete particles hop between neighboring lattice sites at discrete times—accurately reproduce hydrodynamics in the macroscopic limit. These kinds of discrete systems not only provide an intriguing informationdynamics approach to modeling macroscopic physics, but they may also be supremely practical. Exactly the same properties that make these models physically realistic also make them efficiently realizable. Algorithms that incorporate constraints such as locality of interaction and invertibility can be run on microscopic physical hardware that shares these constraints. Such hardware can, in principle, achieve a higher density and rate of computation than any other kind of computer. Thus it is interesting to construct discrete lattice dynamics which are more physicslike both in order to capture more of the richness of physical dynamics in informational models, and in order to improve our ability to harness physics for computation. In this chapter, we discuss techniques for bringing discrete lattice dynamics closer to physics, and some of the interesting consequences of doing so.
Theory of molecular machines. II. Energy dissipation from molecular machines
 J. Theor. Biol
, 1991
"... Single molecules perform a variety of tasks in cells, from replicating, controlling and translating the genetic material to sensing the outside environment. These operations all require that specific actions take place. In a sense, each molecule must make tiny decisions. To make a decision, each “mo ..."
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Cited by 34 (19 self)
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Single molecules perform a variety of tasks in cells, from replicating, controlling and translating the genetic material to sensing the outside environment. These operations all require that specific actions take place. In a sense, each molecule must make tiny decisions. To make a decision, each “molecular machine ” must dissipate an energy Py in the presense of thermal noise Ny. The number of binary decisions that can be made by a machine which has dspace
Solving Highly Constrained Search Problems with Quantum Computers
 Journal of Artificial Intelligence Research
, 1999
"... A previously developed quantum search algorithm for solving 1SAT problems in a single step is generalized to apply to a range of highly constrained kSAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a co ..."
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A previously developed quantum search algorithm for solving 1SAT problems in a single step is generalized to apply to a range of highly constrained kSAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms. 1. Introduction Quantum computers (Benioff, 1982; Bernstein & Vazirani, 1993; Deutsch, 1985, 1989; DiVincenzo, 1995; Feynman, 1986; Lloyd, 1993) offer a new approach to combinatorial search problems (Garey & Johnson, 1979) with quantum parallelism, i.e., the abilit...
Intrinsic Information
 Oxford: University of Oxford
, 1990
"... In everyday usage, information is knowledge or facts acquired or derived from study, instruction or observation. Information is presumed to be both meaningful and veridical, and to have some appropriate connection to its object. Information might be misleading, but it can never be false. Standard in ..."
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In everyday usage, information is knowledge or facts acquired or derived from study, instruction or observation. Information is presumed to be both meaningful and veridical, and to have some appropriate connection to its object. Information might be misleading, but it can never be false. Standard information theory, on the other hand, as developed for communications
The distribution of reversible functions is Normal
 In Genetic Programming Theory and Practise
, 2003
"... The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non zero) chance of perfect solution. Sufficiently good reversible circuits are more c ..."
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Cited by 9 (6 self)
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The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non zero) chance of perfect solution. Sufficiently good reversible circuits are more common. Expected RMS error is also calculated. Random unitary matrices may suggest possible extension to quantum computing. Using the genetic programming (GP) benchmark, the six multiplexor, circuits of Toffoli gates are shown to give a fitness landscape amenable to evolutionary search. Minimal CCNOT solutions to the six multiplexer are found but larger circuits are more evolvable.
Universality of a reversible twocounter machine
 Theoretical Computer Science
, 1996
"... A kcounter machine (CM(k)) is an automaton having k counters as an auxiliary memory. It has been shown by Minsky that a CM(2) can simulate any Turing machine and thus it is universal. In this paper, we investigate the computing ability of reversible (i.e., backward deterministic) CMs. We first show ..."
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A kcounter machine (CM(k)) is an automaton having k counters as an auxiliary memory. It has been shown by Minsky that a CM(2) can simulate any Turing machine and thus it is universal. In this paper, we investigate the computing ability of reversible (i.e., backward deterministic) CMs. We first show that any irreversible CM(R) can be simulated by a reversible CM(k + 2). In this simulation, however, the reversible CM(k + 2) leaves a large number as a garbage in some counter when it halts. We then show that, if k more counters are added, this garbage information is erased reversibly. Finally, we prove that any reversible CM(R) (k = 1,2,3,...) can be simulated by a reversible CM(2). From these results computationuniversality of a reversible CM(2) is established. 1.
DNA Computing: Models and Implementations
, 2002
"... As the fabrication of integrated circuits continues to take place on increasingly smaller scales, we grow closer to several fundamental limitations on electronic computers. For many classes of problems, computing devices based on biochemical reactions present an attractive alternative to conventiona ..."
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Cited by 8 (0 self)
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As the fabrication of integrated circuits continues to take place on increasingly smaller scales, we grow closer to several fundamental limitations on electronic computers. For many classes of problems, computing devices based on biochemical reactions present an attractive alternative to conventional computing paradigms. We present here a survey of the theory and implementation of biologically and biochemically based computers.
Energy complexity of optical computations
 In 2nd IEEE Symposium on Parallel and Distributed Processing
, 1990
"... This paper provides lower bounds on the energy consumption and demonstrates an energytime tradeoff in optical computations. All the lower bounds are shown to have the matching upper bounds for a transitive function – shifting. Since the energy consumption in an optical transmission is a nonlinear ..."
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This paper provides lower bounds on the energy consumption and demonstrates an energytime tradeoff in optical computations. All the lower bounds are shown to have the matching upper bounds for a transitive function – shifting. Since the energy consumption in an optical transmission is a nonlinear function of the distance, a new set of techniques was required to derive these lower bounds. We also characterize the energy requirements of 3D VLSI computations. 1
Automated discovery of selfreplicating structures in cellular automata
 IEEE Trans. Evol. Comp
"... ..."