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22
Oracle quantum computing
 Brassard & U.Vazirani, Strengths and weaknesses of quantum computing
, 1994
"... \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 28 (7 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 22 (15 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
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.
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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Cited by 8 (3 self)
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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
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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Cited by 8 (0 self)
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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...
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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Cited by 8 (4 self)
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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 Space Automata Models
, 1996
"... This thesis demonstrates for the #rst time that it is possible to automatically discover selfreplicating structures in cellular space automata models rather than, as has been done in the past, to design them manually. Selfreplication is de#ned as the process an entity undergoes in constructing a c ..."
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Cited by 4 (3 self)
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This thesis demonstrates for the #rst time that it is possible to automatically discover selfreplicating structures in cellular space automata models rather than, as has been done in the past, to design them manually. Selfreplication is de#ned as the process an entity undergoes in constructing a copy of itself. Von Neumann was the #rst to investigate arti#cial selfreplicating structures and did so in the context of cellular automata, a cellular space model consisting of numerous #nitestate machines embedded in a regular tessellation. Interest in arti#cial selfreplicating systems has increased in recentyears due to potential applications in molecularscale manufacturing, programming parallel computing systems, and digital hardware design, and also as part of the #eld of arti#cial life.
Theory of Thermodynamics of Computation
 Proc. IEEE Physics of Computation Workshop
, 1992
"... We investigate a new research area: we are interested in the ultimate thermodynamic cost of computing from x to y. Other than its fundamental importance, such research has implications for future miniaturization of VLSI chips reducing the energy dissipation below kT (thermal noise), and the similar ..."
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Cited by 3 (1 self)
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We investigate a new research area: we are interested in the ultimate thermodynamic cost of computing from x to y. Other than its fundamental importance, such research has implications for future miniaturization of VLSI chips reducing the energy dissipation below kT (thermal noise), and the similarity distance problem in pattern recognition. It turns out that the theory of thermodynamic cost of computation can be axiomatically developed. Our fundamental theorem connects physics to mathematics, providing the key that makes such a theory possible. It establishes optimal upper and lower bounds on the ultimate thermodynamic cost of computation. By computing longer and longer, the amount of dissipated energy gets closer to these limits. In fact, one can trade time for energy: there is a provable timeenergy tradeoff hierarchy. The fundamental theorem also induces a thermodynamic distance metric. The topological properties of this metric show that neighborhoods are sparse, and get even spar...