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Publications
Publications (61)
Maximum counts of distinct states define important physical quantities, the most famous being entropy. Here we show that energy, momentum and other basic quantities of mechanics are also maximum counts. This generalizes a property familiar in communication with classical waves: frequency-width equals maximum number of distinct values that can be se...
Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a Hilbert phase-space approach we explore quantum speed limits across the quantum to classical transition and identify equivalent bounds in the classical world. As a result, and contrary to common belief, we show that speed limits exist for both quant...
We define, as local quantities, the least energy and momentum allowed by
quantum mechanics and special relativity for physical realizations of some
classical lattice dynamics. These definitions amount to counting rates of local
finite-state change. In two example dynamics, we see that these counts evolve
like classical mechanical energies.
A method for constructing an index suitable for indexing a large set of records identified by long generally randomly distributed record names and for answering membership queries about the set, the method comprising assigning each different record a different record name, determining that a new record name is not already represented in the index b...
A method for organizing a storage system that is scalable and fault tolerant, the method including grouping together a number D of storage elements to form the storage system, where D is more than one, constructing a storage assignment table that includes table entries, computing, for each of the storage elements, an available capacity that depends...
In statistical mechanics, it is well known that finite-state classical
lattice models can be recast as quantum models, with distinct classical
configurations identified with orthogonal basis states. This mapping makes
classical statistical mechanics on a lattice a special case of quantum
statistical mechanics, and classical combinatorial entropy a...
A method for encoding a block of data to allow it to be stored or transmitted correctly in the face of accidental or deliberate modifications, the method including constructing a number n greater than one of original components, each of which is derived from the block and each of which is smaller than the block, and combining original components to...
The usual quantum uncertainty bounds are based on second moments of the quantum amplitude distribution. Here we present similar bounds based on first moments, in which average energy and momentum define the maximum average temporal and spatial rates of distinguishable state change.
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is extended to mechanics, where classical dynamics has traditionally been viewed as a macroscopic approximation of qu...
Fredkin's Billiard Ball Model (BBM) is a continuous classical mechanical model of computation based on the elastic collisions of identical finite-diameter hard spheres. When the BBM is initialized appropriately, the sequence of states that appear at successive integer time-steps is equivalent to a discrete digital dynamics. Here we discuss some mod...
We are concerned with understanding the implicit computation occurring in a physical model of crystal growth, the Reversible Aggregation (RA) model. The RA model is a lattice gas model of reversible cluster growth in a closed two-dimensional system, which captures basic properties of physics such as determinism, locality, energy conservation, and e...
Although not always identified as such, information has been a fundamental quantity in Physics since the advent of Statistical Mechanics, which recognized counting states as the fundamental operation needed to analyze thermodynamic systems. Quantum Mechanics (QM) was invented to fix the infinities that arose classically in trying to count the state...
Fredkin's Billiard Ball Model (BBM) is a continuous classical mechanical model of computation based on the elastic collisions of identical finite-diameter hard spheres. When the BBM is initialized appropriately, the sequence of states that appear at successive integer time-steps is equivalent to a discrete digital dynamics. Here we discuss some mod...
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invarian...
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to each dimension, and with all dimensions treated identically. We show that the model resulting from this techniqu...
This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of discrete systems which incorporate the constraints of locality, uniformity, and exact conservation laws. The features studied include: stochastic nonequ...
Spatial-lattice computations with finite-range interactions are an important class of easily parallelized computations. This class includes many simple and direct algorithms for physical simulation, virtual-reality simulation, agent-based modeling, logic simulation, 2D and 3D image processing and rendering, and other volumetric data processing task...
Results of Feynman and others have shown that the quantum formalism permits a closed, microscopic, and locally interacting system to perform deterministic serial computation. In this paper we show that this formalism can also describe deterministic parallel computation. Achieving full parallelism in more than one dimension remains an open problem....
We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible diffusion limited aggregation model (DLA) in contact with a heat bath. Particles release latent heat when agg...
Discrete lattice systems have had a long and productive history in physics. Examples range from exact theoretical models studied in statistical mechanics to ap- proximate 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 th...
We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time — its maximum speed of dynamical evolution. Previous analyses have given bounds in terms of ΔE, the standard deviation of the energy of the system; here we give a strict bound that depends only on E −...
Reversibility is the only way to compute with asymptotically zero power, and is a novel approach to low power, low energy computing. Recent implementations of reversible and adiabatic [15, 7] logic in standard cmos silicon processes have motivated further research into reversible computing. The application of reversible computing techniques to redu...
The reversible and "adiabatic" transfer of charge in digital circuits has recently been a subject of interest in the low-power electronics community, but no one has yet created a complete, purely reversible CPU using this technology. Fundamental physical scaling laws imply that a fully-reversible processing element would permit unboundedly greater...
An important goal for computer science is to find practical, scalable models of computation that are as efficient as is permitted by the laws of physics. Given a constant upper bound on entropy density, physics implies fundamental constraints on the efficiency of any computation that produces entropy. As a result, it appears that the most efficient...
this paper. This question can be asked with various levels of sophistication. Here we will discuss a particularly simple measure of speed: the maximum number of distinct states that the system can pass through, per unit of time. For a computer, this would correspond to the maximum number of operations per second.
We propose an FPGA chip architecture based on a conventional FPGA logic array core, in which I/O pins are clocked at a much higher rate than that of the logic array that they serve. Wide data paths within the chip are time multiplexed at the edge of the chip into much faster and narrower data paths that run off-chip. This kind of arrangement makes...
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invarian...
For a number of years, we have studied the large-scale fine- grained limit of cellular-logic-array calculations and computers -- with particular emphasis on applications to physical simulation. Perhaps the most relevant lessons of this work for the FPGA community have to do with the applicability of virtual-processor techniques to these logic-array...
The maximum computational density allowed by the laws of physics is available only in a format that mimics the basic spatial locality of physical law. Fine-grained uniform computations with this kind of local interconnectivity (Cellular Automata) are particularly good candidates for efficient and massive micro-physical implementation.
Conventional...
CAM-8 is a mesh-architecture multiprocessor optimized for the large-scale simulation of a wide range of n dimensional Cellular Automata (CA) models-particularly for CA simulations of physical systems. This hardware demonstrates that, for largescale CA computations, purely architectural innovations can lead to about a three order of magnitude cos...
We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular-automata computations. The principal algorithmic innovation is the use of a lattice-gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is...
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above g...
We discuss cellular automata (CA) architectural considerations that led to the design of the cam-8 CA machine; describe some of the spatial modeling tasks that CA's have been applied to on this machine; and discuss some of the interesting practical and theoretical modeling challenges that remain. 1 Introduction For the past 20 years, feature sizes...
Circuit supporting modules form a thre-dimensional communication interconnect mesh. A first embodiment three dimensional communication interconnect is a tetrahedral lattice having a regular, isotropic, thre-dimensional topology in which each module connects to its four physicaly closest neighbors. Thestructure of the tetrahedral interconnect isisom...
Cam-8 is parallel, uniform, scalable architecture offering unprecedented performance in the fine-grained modeling of spatially-extended systems. It provides a general-purpose instrument for the systematic exploration of a new band of the computational spectrum. This brochure is a first attempt at putting under one cover some material that would ill...
A condensed history and theoretical development of lattice-gas automata in the Boltzmann limit is presented. This is provided as background to set up the context for understanding the implementation of the lattice-gas method on two parallel supercomputers: the MIT cellular automata machine CAM-8 and the Connection Machine CM-5. The macroscopic limi...
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect...
As computer hardware makes use of increasingly microscopic physical effects the attractiveness of uniform arrays of simple logic, locally interconnected, becomes correspondingly greater. These kinds of Cellular Automata (CA) based computers can, in principle, achieve a computational density that is near the maximum allowed by the laws of physics. C...
A new approach to polymer simulation well suited to massively parallel architectures is presented. The approach is based on a novel two-space algorithm that enables 50% of the monomers to be updated in parallel. The simplicity of this algorithm enables implementation and comparison of different platforms. Such comparisons are relevant to a wide var...
Hardware manual for CAM-8 cellular automata machine
This chapter discusses fundamental constraints on computing machines that come from physics and some ways that computations can be reorganized to deal with these limits efficiently.
This paper is a manifesto, a brief tutorial, and a call for experiments on programmable matter machines.
In order to improve our ability to simulate the complex behavior of polymers, we introduce dynamical models in the class of Cellular Automata (CA). Space partitioning methods enable us to overcome fundamental obstacles to large scale simulation of connected chains with excluded volume by parallel processing computers. A highly efficient, two-space...
This paper is a manifesto, a brief tutorial, and a call for experiments on programmable matter machines.
Results of Feynman and others have shown that the quantum formalism permits a closed, microscopic, and locally interacting system to perform deterministic serial computation. In this paper we show that this formalism can also describe deterministic parallel computation. Achieving full parallelism in more than one dimension remains an open problem.
The advantages of an architecture optimized for cellular automata simulations are so great that, for sufficiently large-scale CA experiments, it becomes absurd to use any other kind of computer.
In this article we discuss cellular automata machines in general, give some illustrative examples of the use of an existing machine, and then describe a m...
In the light of recent developments in the theory of invertible cellular automata, we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics.
This is the patent on the essential ideas of CAM-8: lattice-gas data movement, which can be accomplished by changing pointers addressing memory, and table lookup processing. Virtual SIMD processing, where the fine-grained updates are simulated using large memories for both data and processing, can be extremely efficient and powerful. The virtualiza...
We point out the advantages of computing the dynamics of Ising spin glasses and related (e.g., bond or site dilution) systems in zero external field by using bond-energy variables bij=sisjJij instead of the usual spin variables and coupling constants.
PhD Thesis, Massachusetts Institute of Technology, Dept. of Physics, June 1987, reprinted in March 1988 as an MIT Technical Report. The thesis itself is available online from MIT DSpace with the permanent handle http://hdl.handle.net/1721.1/14862
Physics imposes fundamental constraints on the ultimate potentialities of computing mechanisms.
The most prominent fundamental constraint coming from physics that is felt today is the finiteness of the speed of light. This constraint implies that communication paths inside of a computer should be as short as possible. For maximum speed, we would a...
Recently, cellular automata machines with the size, speed, and flexibility for general experimentation at a moderate cost have become available to the scientific community. These machines provide a laboratory in which the ideas presented in this book can be tested and applied to the synthesis of a great variety of systems. Computer scientists and r...
A computer is a physical system which has a very general ability to simulate other physical systems (and in particular, other computers). In this paper we investigate the question of whether microscopic quantum systems can be computers. Using a reversible cellular automaton model of computation we illustrate several approaches to this question. We...
We report recent developments in the modeling of fluid dynamics, and give experimental results (including dynamical exponents) obtained using cellular automata machines. Because of their locality and uniformity, cellular automata lend themselves to an extremely efficient physical realization; with a suitable architecture, an amount of hardware reso...
Reversible Cellular Automata are computer-models that embody discrete analogues of the classical-physics notions of space, time, locality, and microscopic reversibility. They are offered as a step towards models of computation that are closer to fundamental physics.
