Meta tags:
description=Physics blog quantum computation;
keywords=Physics blog forum quantum computation science books lectures universe cosmology theory teleportation mind body;

Headings (most frequently used words):

latest, strange, paths, canon, atomic, orbital, reversible, computation, marangoni, flow, water, clouds, classical, molecules, languages, posts, comments, categories, resources, archives, links, blogs, meta,

Text of the page (most frequently used words):
the (178), and (53), #computation (39), #reversible (26), quantum (23), are (22), this (21), that (20), with (17), states (16), state (15), system (15), irreversible (15), physics (12), for (11), into (11), physical (11), paths (10), comments (10), two (10), model (10), information (10), not (9), 2007 (9), classical (9), which (9), then (9), any (9), its (9), since (8), from (8), between (8), also (8), bennett (8), computing (8), may (8), function (8), output (8), input (8), machine (7), week (7), gallery (7), about (7), canon (7), italiano (7), français (7), languages (7), when (7), first (7), principle (7), other (7), xantox (7), turing (7), logical (7), demon (7), toffoli (7), example (7), events (7), one (7), space (7), all (6), philosophy (6), new (6), january (6), read (6), water (6), flow (6), molecules (6), share (6), dynamics (6), known (6), image (6), error (6), universal (6), entropy (6), reversibility (6), irreversibility (6), gate (6), would (6), where (6), path (6), mathematical (5), 2008 (5), clouds (5), marangoni (5), atomic (5), orbital (5), their (5), like (5), journal (5), lecerf (5), was (5), landauer (5), process (5), possible (5), logically (5), computational (5), rss (4), entries (4), finds (4), dna (4), while (4), john (4), english (4), charges (4), initial (4), very (4), they (4), dipoles (4), click (4), zoom (4), surface (4), tension (4), method (4), heat (4), feynman (4), fredkin (4), billiard (4), ball (4), logic (4), errors (4), step (4), until (4), but (4), finite (4), embedding (4), time (4), following (4), back (4), strange (3), april (3), news (3), fun (3), baez (3), 291 (3), per (3), has (3), light (3), electron (3), without (3), liquid (3), over (3), argument (3), mit (3), allowed (3), evolve (3), quickly (3), there (3), der (3), force (3), can (3), eventually (3), animation (3), showing (3), spheres (3), same (3), motion (3), stable (3), cloud (3), producing (3), each (3), result (3), interactions (3), thermodynamics (3), only (3), inverse (3), write (3), machines (3), brownian (3), maxwell (3), automata (3), however (3), systems (3), environment (3), such (3), computations (3), models (3), gates (3), memory (3), temperature (3), escher (3), closed (3), energy (3), dissipation (3), final (3), mechanics (3), right (3), lost (3), mapping (3), whose (3), evolution (3), your (2), address (2), mail (2), technorati (2), web (2), del (2), 2006 (2), rights (2), reserved (2), add (2), meta (2), brain (2), plus (2), astronomy (2), blogs (2), march (2), july (2), september (2), 2009 (2), papers (2), books (2), lectures (2), resources (2), non (2), seen (2), through (2), latest (2), produced (2), surfaces (2), experiment (2), replication (2), limit (2), entanglement (2), genomes (2), cannot (2), established (2), works (2), subtlety (2), than (2), 2004 (2), coulomb (2), unbalanced (2), large (2), much (2), interaction (2), repulsive (2), attractive (2), bound (2), mechanism (2), some (2), particles (2), interact (2), represented (2), mechanical (2), origin (2), shown (2), allowing (2), them (2), university (2), air (2), according (2), results (2), cooling (2), droplets (2), appearance (2), thickness (2), several (2), effects (2), über (2), die (2), einer (2), phys (2), different (2), these (2), forces (2), cause (2), patterns (2), found (2), film (2), both (2), leading (2), correcting (2), exist (2), theory (2), computer (2), szilard (2), 1929 (2), translation (2), decrease (2), intelligent (2), des (2), sciences (2), paper (2), work (2), after (2), shift (2), quintuple (2), ibm (2), res (2), dev (2), related (2), generation (2), devised (2), save (2), reverse (2), reversibly (2), international (2), theoretical (2), 1982 (2), 1961 (2), cellular (2), sources (2), consequence (2), performing (2), erroneous (2), erasure (2), kinds (2), affecting (2), chaotic (2), more (2), unitary (2), transformations (2), solution (2), who (2), molecule (2), position (2), standard (2), dissipative (2), room (2), observing (2), small (2), always (2), used (2), backwards (2), least (2), perform (2), amount (2), event (2), end (2), thermal (2), reaches (2), tape (2), perturbations (2), correction (2), based (2), laws (2), equivalent (2), defined (2), various (2), primitives (2), proposed (2), meaning (2), terms (2), another (2), forward (2), nand (2), every (2), relationship (2), theorem (2), implies (2), performs (2), must (2), bearing (2), case (2), side (2), left (2), boolean (2), graph (2), latin (2), given (2), within (2), move (2), single (2), musical (2), universe (2), home (2), name, tailrank, windows, live, reddit, gnolia, newsvine, blinklist, google, bookmarks, stumbleupon, yahoo, netscape, furl, digg, icio, social, close, copyright, present, bloglines, favorites, atom, antimeta, garden, forking, lemmings, experimental, brains, neurophilosophy, fragments, consciousness, conscious, entities, pains, hammer, neighborhood, infinity, shtetl, optimized, magazine, what, terence, tao, noncommutative, geometry, mathematics, under, microscope, michael, nielsen, learning, category, café, ars, mathematica, backreaction, metadatta, theorema, egregium, even, wrong, bad, blog, systemic, pontiff, cosmic, variance, mathworld, stanford, encyclopedia, arxiv, links, december, february, archives, scientists, webpages, resource, websites, recent, fundamental, online, categories, stupendo, sopratutto, vedere, differenza, delle, anastasia, replicazione, idem, egb, unisco, complimenti, gian, luca, rivalta, applausi, che, dire, una, marco, gamarra, fantastico, questo, sarà, sicuramente, utilissimo, apporto, mimma, macheda, canone, why, circular, symetry, informatimago, sun, earth, neutrino, bravo, merci, pour, cet, article, fascinant, olivier, arche, interstellaire, vulgarisation, concepts, complexes, est, pierre, thomas, calcul, réversible, crystals, interstellar, ark, caustics, total, lunar, eclipse, eraser, chromosome, observation, jupiter, moons, 1613, placed, photon, charge, axions, confirmed, pvlas, teleportation, shared, bouncing, jets, inside, posts, francis, bacon, novum, organum, 1620, axioms, argumentation, should, avail, discovery, nature, greater, many, times, previous, belcher, teal, studio, project, thing, happens, attraction, pair, off, thereafter, still, weaker, neighboring, van, waals, although, either, torque, rotates, bringing, together, binds, substances, solid, four, equal, mass, positive, negative, approximation, electromagnetism, via, mediated, electric, field, yellow, pauli, becomes, critical, distance, radius, keeps, collapsing, point, additionally, damped, term, proportional, velocity, settle, down, sarah, robinson, colorado, visualization, course, pruppacher, klett, springer, 1997, houze, academic, press, 1994, microphysics, precipitation, kind, convective, cumulus, vertical, winds, occurring, regions, warm, moist, archimedes, rapid, lifting, adiabatic, expansion, consequent, accretion, irregular, distribution, scatters, sunlight, geometrically, directions, bright, white, snow, decaying, gray, shades, optical, short, lived, lasting, approximately, minutes, average, terrestrial, extraordinarily, complex, feedback, mechanisms, combining, fluid, fischer, darhuber, troian, department, chemical, engineering, princeton, ausbreitung, tropfen, flüssigkeit, auf, oberfläche, anderen, ann, leipzig, 143, 337, 354, 1871, pulled, boundary, layers, get, contact, effect, beautiful, ancient, japanese, art, floating, ink, oleic, acid, surfactant, spreads, spontaneously, layer, glycerol, capillary, stresses, variations, dendritic, contour, lines, interference, fringes, suminagashi, intermolecular, calderbank, shor, rev, 1098, 1105, 1996, good, codes, deutsch, proc, roy, soc, lond, a400, 117, 1985, foundation, church, zeitschrift, für, physik, 840, 856, behavioral, science, 301, 310, 1964, thermodynamic, intervention, beings, entropieverminderung, einem, thermodynamischen, bei, eingriffen, intelligenter, wesen, frank, comptes, rendus, hebdomadaires, séances, académie, 257, 2597, 2600, 1963, unrelated, issues, sought, design, proposing, saving, history, decomputing, away, though, had, initially, little, impact, discovered, perhaps, because, published, himself, did, emphasize, minor, flaw, sort, namely, réversibles, 525, 1973, problem, connection, explored, proved, simulated, 905, 940, review, 1984, 1986, perseus, 2000, 219, 253, conservative, tech, memo, lcs, 151, lab, comp, sci, 1980, 183, wuensche, lesser, ref, vol, santa, institute, studies, complexity, addison, wesley, 1992, images, transition, graphs, global, thank, charles, stimulating, draft, affected, loss, coherence, correct, generic, reconstruct, free, price, less, susceptible, certains, discrete, spectrum, prevents, trajectories, becoming, reliable, counterpart, takes, advantage, superposition, qualitatively, paradigm, occur, important, toward, controversial, paradox, taken, avoiding, dualistic, traps, substituting, simple, suggested, proper, accounting, restored, measuring, explanation, became, 1981, showed, fundamentally, surprisingly, measurement, done, make, measurements, 1867, thought, involving, microscopic, capable, individual, guards, hole, separating, containers, filled, gas, approaches, checks, speed, opens, closes, shutter, slower, container, faster, heating, apparent, violation, 2nd, law, swans, 1956, company, netherlands, permission, www, mcescher, com, shall, compute, twice, forwards, obtain, second, mirror, returning, seemed, rule, out, possibility, useful, remarkable, earlier, anticipated, formal, unlimited, insufficient, build, physically, growing, needing, replicated, saturate, come, unless, irreversibly, erased, have, been, merely, postponed, avoided, reversal, stabler, approach, noise, contrary, freely, near, equilibrium, potential, barriers, define, walks, randomly, rna, polymerase, enzyme, involved, transcription, copying, follows, similar, adds, practice, unreliable, instability, arising, arbitrarily, generate, deviations, saturated, corrected, adding, potentials, stabilize, itself, erase, hence, appears, aspect, defining, lower, detects, switch, invented, focusing, implementation, components, formalism, kinetic, perfect, gases, presence, moving, rigid, specified, points, absence, means, angle, collisions, allow, construct, due, ressler, version, railroad, switches, constructed, primitive, exchanges, inputs, depending, third, control, thus, embed, conditional, routing, carrying, conserved, signals, additional, bits, ariadne, threads, ensure, reversed, garbage, program, instead, losing, kept, controlled, above, embedded, bijection, original, indicated, red, further, noticed, transformed, larger, replicating, sinks, intrinsically, nondissipative, bears, carnot, engine, most, efficient, engines, ones, clausius, attributing, zero, change, processes, studied, thermodynamical, increase, absolute, minimum, release, bit, boltzmann, constant, joules, emphasizes, facts, precisely, reduces, increasing, representing, part, lagrangian, hamiltonian, bijective, invertible, indicates, stay, tries, depict, mapped, onto, impossible, knowing, find, algebra, set, functions, xor, map, merging, longer, deterministic, said, revertere, turn, determine, permutation, conservation, prepared, labeled, discretized, directed, nodes, edges, transforming, order, robust, label, observed, choosen, correspondence, sufficiently, respect, definition, formulated, automaton, complete, sequence, symbols, head, internal, symbol, successive, deterministically, combination, elementary, motions, computare, count, cut, abstract, representation, transitions, dean, dauger, hydrogenic, numbers, schrödinger, equation, colors, represent, phase, matter, electrons, orbiting, nucleus, follow, determined, visualized, probabilities, location, created, pov, ray, music, performed, post, flemish, harpsichord, upper, manual, jos, leys, enigmatic, bach, offering, 1747, crab, cancrizans, manuscript, shows, score, beginning, joins, topologically, bundle, line, segment, circle, möbius, strip, simultaneous, performance, deeply, backward, gives, voices, symmetry, determines, built, unplayed, silence, forum, early,

Text of the page (random words):
oosen correspondence is sufficiently stable in respect to various kinds of perturbations the system is then prepared in an initial state and is allowed to evolve through a path of events within the space of states until it eventually reaches a state labeled as final the discretized dynamics of the computational space may be represented with a directed graph where nodes are possible states of the system and edges are events transforming a state into another irreversible computational dynamics click image to zoom 1 logical reversibility a function is said reversible from latin revertere to turn back if given its output it is always possible to determine back its input which is the case when there is a one to one relationship between input and output states if the space of states is finite such a function is a permutation logical reversibility implies conservation of information when several input states are mapped onto the same output state then the function is irreversible since it is impossible by only knowing the final state to find back the initial state in boolean algebra not is reversible while set to one is irreversible two argument boolean functions like and or xor are also irreversible since they map 2 2 input states into 2 1 output states so that information is lost in the merging of paths like shown in the following graph of a nand computation whose reverse evolution is no longer deterministic the right side tries to depict the inverse mapping to the left side physical reversibility known laws of physics are reversible this is the case both of classical mechanics based on lagrangian hamiltonian dynamics and of standard quantum mechanics where closed systems evolve by unitary transformations which are bijective and invertible as a consequence when a physical system performs an irreversible computation the computation model s mapping indicates that the computing system cannot stay closed more precisely since an irreversible computation reduces the space of physical information bearing states then their entropy must decrease by increasing the entropy of the non information bearing states representing the thermal part of the system in 1961 landauer studied this thermodynamical argument and proposed the following principle if a physical system performs a logically irreversible classical computation then it must increase the entropy of the environment with an absolute minimum of heat release of kt x ln 2 per lost bit where k is boltzmann s constant and t the temperature ie about 3 x 10 21 joules at room temperature 2 which emphasizes two facts the logical irreversibility of a computation implies the physical irreversibility of the system performing it information is physical logically reversible computations may be at least in principle intrinsically nondissipative which bears a relationship with carnot s heat engine theorem showing that the most efficient engines are reversible ones and clausius theorem attributing zero entropy change to reversible processes reversible embedding of irreversible computations landauer further noticed that any irreversible computation may be transformed into a reversible one by embedding it into a larger computation where no information is lost eg by replicating every output in the input sources and every input in the output sinks for example the nand irreversible function seen above may be embedded in the following bijection also known as toffoli gate 3 the original function is indicated in red the additional bits of information like ariadne s threads ensure that any computational path may be reversed they are the garbage of the forward path and the program of the backwards path instead of losing them in the environment they are kept in the controlled computational space toffoli gates are universal reversible logic primitives meaning that any reversible function may be constructed in terms of toffoli gates the fredkin gate is another example of universal reversible logic primitive it exchanges its two inputs depending on the state of a third control input thus allowing to embed any computation into a conditional routing of paths carrying conserved signals some railroad switches are reversible reversible computation models the billiard ball model invented by fredkin and toffoli 4 was one of the first computation models focusing on implementation with reversible physical components based on the laws of classical mechanics it is equivalent to the formalism of kinetic theory of perfect gases the presence of moving rigid spheres at specified points are defined as 1 s their absence as 0 s interactions by means of right angle collisions allow to construct various logic primitives like for example the following 2 input 3 output universal gate due to feynman 5 who also proposed with ressler a billiard ball version of the fredkin gate feynman switch gate b detects a without affecting its path in practice these computing spheres would be very unreliable as instability arising from arbitrarily small perturbations would quickly generate chaotic deviations producing an output saturated with errors the errors may be corrected for example by adding potentials to stabilize the paths however the error correction process is itself irreversible and dissipative since it has to erase the erroneous information hence error correction appears to be the only aspect of computation defining a lower bound to energy dissipation a stabler approach is that of the brownian computation model 6 where thermal noise is on the contrary allowed to freely interact with a computing system near equilibrium potential energy barriers define the paths of a computational space where the system walks randomly until it eventually reaches a final state rna polymerase the enzyme involved in dna transcription is an example of a brownian logically reversible tape copying machine the dna replication process also follows a similar mechanism but adds a logically irreversible error correcting step lecerf bennett reversal the embedding method is however insufficient to build a physically reversible universal computer since the growing amount of information needing to be replicated for each event would saturate any finite memory then computation would come to an end unless the memory would be irreversibly erased but then dissipation would have been merely postponed and not avoided this seemed to rule out the possibility of useful reversible computing machines until a remarkable solution was found by bennett 7 earlier work by lecerf 8 anticipated its formal method showing that it is possible at least in principle to perform an unlimited amount of computation without any energy dissipation the reversible system shall compute the embedding function twice the first time forwards to obtain and save the computation result and the second time backwards as a mirror image computation of the inverse function de computing the first step and returning the closed system to its initial state m c escher swans 1956 all m c escher works c 2007 the m c escher company the netherlands all rights reserved used by permission www mcescher com click image to zoom logical irreversibility and maxwell s demon in 1867 maxwell devised a thought experiment involving a finite microscopic demon capable of observing the motion of individual molecules this demon guards a small hole separating two containers filled with gas at the same temperature when a molecule approaches the demon checks its speed and then opens or closes a shutter so as slower molecules always go in one container cooling it and faster molecules go in the other heating it in apparent violation of the 2nd law of thermodynamics a first important step toward the solution of this controversial paradox was taken in 1929 by szilard 9 who after avoiding dualistic traps by substituting the intelligent demon with a simple machine suggested that proper accounting of entropy is restored in the process of measuring the molecule position this explanation became the standard one until 1981 when bennett showed 6 that the fundamentally dissipative step is surprisingly not the measurement which can be done reversibly but the logically irreversible erasure of demon s memory to make room for new measurements reversibility in quantum computation quantum computation takes advantage of the physical effects of superposition and entanglement leading to a qualitatively new computation paradigm 10 in quantum mechanical computation models all events occur by unitary transformations so that all quantum gates are reversible quantum systems are less susceptible to certains kinds of errors affecting classical computations since their discrete spectrum prevents trajectories from becoming chaotic so that for example a quantum billiard ball model is more reliable than its classical counterpart however quantum systems are also affected by new sources of error as a consequence of interactions with the environment such as the loss of quantum coherence it is possible to correct generic quantum errors up to a limit 11 so as to reconstruct an error free quantum state at the price of performing an irreversible quantum erasure of the erroneous quantum information i thank charles h bennett for stimulating comments on the draft a wuensche m lesser the global dynamics of cellular automata ref vol i of the santa fe institute studies in the sciences of complexity addison wesley 1992 images of cellular automata state transition graphs r landauer irreversibility and heat generation in the computing process ibm journal of res and dev 5 3 183 1961 logical irreversibility landauer s principle t toffoli reversible computing tech memo mit lcs tm 151 mit lab for comp sci 1980 toffoli gate reversible automata e fredkin t toffoli conservative logic international journal of theoretical physics 21 3 4 219 253 1982 billiard ball model r p feynman feynman lectures on computation 1984 1986 perseus books 2000 c h bennett the thermodynamics of computation a review international journal of theoretical physics 21 12 905 940 1982 brownian computation model logical irreversibility and maxwell s demon c h bennett logical reversibility of computation ibm journal of res and dev 17 6 525 1973 in this paper related to the problem of the connection between computing and heat generation explored by landauer bennett devised the save result and reverse method and proved that any irreversible computation may be simulated reversibly y lecerf machines de turing réversibles english translation by m frank reversible turing machines comptes rendus hebdomadaires des séances de l académie des sciences 257 2597 2600 1963 in this mathematical paper unrelated to issues of physical reversibility lecerf sought to design a reversible turing machine it is the first work proposing the method of saving the computation history and then decomputing it away though it had initially little impact and was discovered only much after bennett s results perhaps because it was not published in english and lecerf himself did not emphasize it it has a minor flaw ie the inverse of a read write shift quintuple is a quintuple of different sort namely shift read write l szilard über die entropieverminderung in einem thermodynamischen system bei eingriffen intelligenter wesen journal zeitschrift für physik 53 840 856 1929 english translation on the decrease of entropy in a thermodynamic system by the intervention of intelligent beings in behavioral science 9 4 301 310 1964 d deutsch quantum theory the church turing principle and the universal quantum computer proc roy soc lond a400 97 117 1985 foundation of the quantum model of computation universal quantum turing machine a r calderbank p w shor good quantum error correcting codes exist phys rev a 54 1098 1105 1996 5 comments share this marangoni flow xantox 6 january 2008 in gallery other languages français italiano liquid surfaces are pulled by the intermolecular forces which are unbalanced on the boundary producing surface tension when liquid layers with different surface tension get in contact these forces cause a flow also known as marangoni effect 1 which is also the origin of the beautiful patterns found in the ancient japanese art of suminagashi floating ink in this image a film of oleic acid surfactant with surface tension 32 5 mn m quickly spreads spontaneously about 2 5 mm over a layer of glycerol with surface tension 63 4 mn m both marangoni and capillary stresses cause variations in the film thickness leading to dendritic flow patterns the contour lines are interference fringes click image to zoom 2 c marangoni über die ausbreitung der tropfen einer flüssigkeit auf der oberfläche einer anderen ann phys leipzig 143 337 354 1871 b j fischer a a darhuber s m troian department of chemical engineering princeton university comments share this water clouds xantox 17 september 2007 in gallery other languages français italiano terrestrial clouds are the result of extraordinarily complex interactions between water and air with several feedback mechanisms combining the effects of fluid dynamics and thermodynamics 1 click image to zoom 2 the kind of convective clouds known as cumulus are produced by the vertical winds occurring in regions of warm moist air according to archimedes principle the rapid lifting results in adiabatic expansion and cooling and consequent accretion of water droplets the irregular distribution of droplets scatters sunlight geometrically in all directions producing a bright white appearance like in snow decaying into gray shades as per their optical thickness each cloud is short lived lasting approximately 15 minutes in average h r pruppacher j d klett microphysics of clouds and precipitation springer 1997 r a houze cloud dynamics academic press 1994 2004 sarah robinson flow visualization course university of colorado comments share this classical molecules xantox 9 july 2007 in gallery other languages français italiano animation showing the interaction of four charges of equal mass 1 two positive and two negative in the approximation of classical electromagnetism the particles interact via the coulomb force mediated by the electric field represented in yellow a repulsive pauli force of quantum mechanical origin which becomes very large at a critical distance of about the radius of the spheres shown in the animation keeps the charges from collapsing into the same point additionally the motion of the particles is damped by a term proportional to their velocity allowing them to settle down into stable or meta stable states when the charges are allowed to evolve from the initial state the first thing that happens very quickly since the coulomb attraction between unbalanced charges is very large is that they pair off into dipoles thereafter there is still a much weaker interaction between neighboring dipoles van der waals force although in principle it can be either repulsive or attractive there is a torque that rotates the dipoles so t...