Physics-like models of computation

Margolus, Norman

doi:10.1016/0167-2789(84)90252-5

Cited by 318 publications

(167 citation statements)

References 5 publications

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“…The paradigm originates from computational universality of Game of Life [11], conservative logic and billiard-ball model [14] and their cellular-automaton implementations [16].…”

Section: Dynamical Versus Structural Computationmentioning

confidence: 99%

Experimental implementation of collision-based gates in Belousov–Zhabotinsky medium

Costello

Adamatzky

2005

Chaos, Solitons & Fractals

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“…The paradigm originates from computational universality of Game of Life [11], conservative logic and billiard-ball model [14] and their cellular-automaton implementations [16].…”

Section: Dynamical Versus Structural Computationmentioning

confidence: 99%

Experimental implementation of collision-based gates in Belousov–Zhabotinsky medium

Costello

Adamatzky

2005

Chaos, Solitons & Fractals

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“…Computations may be supported by many different systems (1,2), including physical systems like the digital computer, Fredkin logic gates (3), billiard-ball collisions (4), enzymes operating on a polymer chain (1,5), and more abstract systems like cellular automata (6)(7)(8), partial differential equations that simulate cellular automata (9), generalized shifts (4), and neural networks (10)(11)(12)(13). Some of these systems can be computationally universal and thus are formally equivalent with a universal Turing machine (10,14).…”

Section: Introductionmentioning

confidence: 99%

Chemical implementation of neural networks and Turing machines.

Hjelmfelt

Weinberger

Ross

1991

Proc. Natl. Acad. Sci. U.S.A.

245

175

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We propose a reversible reaction mechanism with a single stationary state in which certain concentrations assume either high or low values dependent on the concentration of a catalyst. The properties of this mechanism are those of a McCulloch-Pitts neuron. We suggest a mechanism of interneuronal connections in which the stationary state of a chemical neuron is determined by the state of other neurons in a homogeneous chemical system and is thus a "hardware" chemical implementation of neural networks. Specific connections are determined for the construction of logic gates: AND, NOR, etc. Neural networks may be constructed in which the flow oftime is continuous and computations are achieved by the attainment of a stationary state of the entire chemical reaction system, or in which the flow of time is discretized by an oscillatory reaction. In another article, we will give a chemical implementation of finite state machines and stack memories, with which in principle the construction of a universal Turing machine is possible.Computations may be supported by many different systems (1, 2), including physical systems like the digital computer, Fredkin logic gates (3), billiard-ball collisions (4), enzymes operating on a polymer chain (1, 5), and more abstract systems like cellular automata (6-8), partial differential equations that simulate cellular automata (9), generalized shifts (4), and neural networks (10-13). Some of these systems can be computationally universal and thus are formally equivalent with a universal Turing machine (10,14). We may inquire about whether computationally universal devices may be constructed solely from chemical reaction mechanisms in a homogeneous medium. All living entities process information to varying degrees, and this can occur only by chemical means. It is for this reason alone that the subject is ofinterest. In this article, we discuss the construction of chemical networks where coupled reaction mechanisms implement "programmed" computations as the concentrations evolve in time. It has already been noted that bistable chemical systems are in many ways analogous to a flip-flop circuit, by coupling bistable reactions it is possible to build universal automata (15,16), and that various chemical mechanisms share a formal relationship with electronic devices (17, 18). We address the construction of computational devices from the viewpoint of neural networks. We propose a chemical reaction network, which is a "hardware" implementation of a neural network, and hence the network can in principle be as powerful as a universal Turing machine (10).Neural networks are a versatile basis for computation (19). Any finite state machine, and hence the finite state part of a universal Turing machine, can be simulated by a neural network (10,20). Neural networks also form the basis of many collective computational systems such as feedforward networks or Hopfield's network (11-13). A chemical neural network may serve as the "hardware" for any of the approaches to computation. We present hardw...

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“…The cellular automaton model. Quantum cellular automata (discrete, translationally invariant, causal evolutions on a lattice) were first envisaged as computational models [25] and quantum simulators [26], although they have by now attracted attention both as hardware for specific quantum information processing tasks [27] and as models of causal quantum theories, including quantum field theory [28,29] and quantum gravity [30]. Such aims have focused on unitary automata, whose extension to more general CP-maps is little explored [31].…”

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confidence: 99%

Noisy Quantum Cellular Automata for Quantum versus Classical Excitation Transfer

Avalle

Serafini

2014

Phys. Rev. Lett.

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*We introduce a class of noisy quantum cellular automata on a qubit lattice that includes all classical Markov chains, as well as maps where quantum coherence between sites is allowed to build up over time. We apply such a construction to the problem of excitation transfer through 1-d lattices, and compare the performance of classical and quantum dynamics with equal local transition probabilities. Our discrete approach has the merits of stripping down the complications of the open system dynamics, of clearly isolating coherent effects, of allowing for an exact treatment of conditional dynamics, all while capturing a rich variety of dynamical behaviours. PACS numbers: 03.65.Yz, 03.65.Aa, Quantifying the extent to which quantum coherence enhances the performance of antennae or communication systems is a timely [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], yet often controversial, subject. Typically, a classical system is compared to the analogous, quantised model [12,13,[20][21][22], although such a correspondence is not straightforward when open, dissipative systems are considered, as it should be in most cases of interest.In this manuscript, we introduce a strictly local model of energy transfer via a noisy quantum cellular automaton construction [23,24] on a qubit lattice. Tuning one real parameter of such a model will allow us to range from a classical Markov chain, where quantum coherence is systematically suppressed at each time-step of the automaton, to dynamics where quantum coherence is allowed to build up over time, while keeping, by construction, the local transition probabilities constant. Thus, a "fair" comparison between classical and quantum energy transfer may be carried out, where the effect of quantum interference is singled out with no ambiguity. Our model, restricted to the first excitation subspace, can be studied exactly for very large systems, also including conditional dynamics due to measurements (which will model the absorption of the excitation at the end of the energy transfer process).The plan of the paper is as follows. We shall first consider the problem of constructing a class of one-qubit completely positive (CP) maps that, in a certain limit, reproduce all classical Markov transition matrices on dichotomic probability distributions. We will then apply our construction to the first excitation subspace of a partitioned quantum cellular automaton structure (where one-qubit maps will be applied to the two-dimensional space spanned by excitations at neighbouring sites), obtaining a global dynamics on a lattice which is capable of describing excitation transfer. We will then present a study of the performance of classical versus quantum maps, showing by how much and under what conditions does quantum coherence improve the probability of excitation transfer through the lattice. Finally, we shall draw some conclusions and discuss outlook of this work. Let us remind the reader that the matrix (and map) T p,q is referred to as doubly stochastic if p = q. Any classical...

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Physics-like models of computation

Cited by 318 publications

References 5 publications

Experimental implementation of collision-based gates in Belousov–Zhabotinsky medium

Experimental implementation of collision-based gates in Belousov–Zhabotinsky medium

Chemical implementation of neural networks and Turing machines.

Noisy Quantum Cellular Automata for Quantum versus Classical Excitation Transfer

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