quantum cellular automata...
TRANSCRIPT
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QuantumCellularAutomata(QCA)AndrewValesky
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PresentationSchedule
•QuantumObservations(5min)
•CellularAutomata(5min)
•QuantumCellularAutomata(10min)
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• PythagorasofSamos
• PythagoreanTheorem
• Pythagoreanism
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Flatland:ARomanceofManyDimensions
• EdwinAbbotAbbot (1884)• womenareline-segments• menarepolygons(n-sided)• forhecannotconceiveofanyotherexcepthimself – andplumeshimselfuponthevarietyof ItsThought asaninstanceofcreativePower.LetusleavethisGodofPointland totheignorantfruitionofhisomnipresenceandomniscience.~(theSphere)
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TheQuantumMind
• Hyperspace:AScientificOdysseyThroughParallelUniverses,TimeWarps,andthe10thDimension• Michio Kako
• Human’sseein3dimensions• Noadvantagetoseeinotherdimentions• Evolutionarysurvival
• Mustourmindsworkin3dimensions?
• QuantumProbabilityinCognition• Dr.MacLennan
• TheoriesofCognition• Logic
• Aristotle’stime
• ClassicalProbability• 1970
• QuantumProbability
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• CollectiveUnconscious• Jung1916
• dreams,fantasies,andotherexceptionalstatesappearnatively
• primordialimagesorarchetypes,asIhavecalledthem,belongtothebasicstockoftheunconsciouspsycheandcannotbeexplainedaspersonalacquisitions• Collectivelycalledthecollectiveunconscious
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Michelangelo'sCreationofAdam
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Aoccdrnig to a rscheearch at CmabrigdeUinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihngis taht the frist and lsat ltteer be at the rghitpclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseaethe huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.
According to a researcher (sic) at Cambridge University, it doesn't matter in what order the letters in a word are, the only important thing is that the first and last letter be at the right place. The rest can be a total mess and you can still read it without problem. This is because the human mind does not read every letter by itself but the word as a whole.
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CellularAutomata
• JohnvonNeumann• “Whatkindoflogicalorganizationissufficientforanautomatontoreproduceitself?”• 1903
• RegularGridofcells• Finitenumberofstatesforeachgrid• N-dimensional• Neighborhooddefinedforeachcell• Initialstatedefinedforeachcell• Achangingfunctionforeachcell• Basedonneighborhood• Usuallysameforeachcell
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ProcessingImageofGameoflife
ProcessingImageofSpiernsky Triangle
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GameofLife
• JohnConway1970• Infinitetwo-dimensionalorthogonalgridofcells• Twopossiblestates• Rules(functionorchangingcells)• Livingcellwithfewerthantwoliveneighbours dies• livingcellwithtwoorthreeliveneighbours liveson• Livingcellwithmorethanthreeliveneighbours dies• Deadcellwithexactlythreeliveneighbours becomesalivecell
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CellularAutomata?
• TuringComplete
• EdgeofChaos
• Applicationstootherfields
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Rule110:CellularAutomata
• TuringComplete• SimulateasingletapedTuringMachine• Computable
• EdgeofChaos• Lambdavalue
• 0=order• 1=chaos
01101110
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Miller– UreyExperiment
• Createearlyearthconditions• methane (CH4)• water (H2O)• ammonia (NH3)• hydrogen (H2)• ContinuousElectricSparks
• AminoAcidswerecreated• Protein• 20+
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QuantumCellularAutomata
• Generalizationofcellularautomata(CA)• ReversibleCA• GrössingG,ZeilingerA(1988)Quantumcellularautomata• Noagreedupondefinition
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CellularAutomatavsQuantumCellularAutomata
• (CA)isa4-tuple(L,Σ,N,f) • (QCA)isa3-tuple(L,H,U)
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PartitionedWatrous QCA
• Firstproofofcomputationaluniversality• GivenanyquantumTuringMachine,thereexistsaPWQCAwhichsimulatestheTuringMachinewithConstantslowdown• GivenanyPWQCA,thereexistsaTuringMachinewhichsimulatesthePWQCAwithlinearslowdown
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TypesofQCA
• Reversible• LocalUnitary• 1dimensional• UniversalSimulateanyquantumcircuit• Canbesimulatedusingafamilyofquantumcircuits
• BlockPartitioned• ContinuousTime• Hamiltonian
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QCAExploration• LogicalDevicesusingQCA
• QuantumDots• Xor• adder
• QuantumTuringMachinesarestilltheoretical• Confinedtoaveryfinitenumberofelements
• Opticallattices• Artificialcrystalsoflightandconsistsofmicrotraps• Crossed laser beams,
• creatingpolarizationpattern• Atomscoolandcongregateintheminima
• Resemblesacrystallattice• Quantumtunnelingcanoccur
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QuantumLatticeGasAutomata
• partialdifferentialequationcanbetheevolutionofsomeCA• CAwillmimicthepartialdifferentiationequation• Continuoustimelimit• Continuousspacelimit
• QLGAhasdemonstratedtheequivalence• EvolutionofsetofquantumlatticeBoltzman equations
• Exploredtomodelphysicalsystems
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QuantumTunneling
• Wave-ParticleDuality• Particle• Classicalmechanics• Sumofenergy
• Wave• Quantummechanics
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QuantumTunneling• Thematterridesthewave
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QuantumDotAutomata
• QuantumDots• Consistofnanoparticles• 5quantumdots• Twoelectrons
• Dotshopamongthefivestates• Electronsfindfarthestdistance
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WorksCited
• Availableuponrequest