QuantumCellularAutomata(QCA)AndrewValesky

PresentationSchedule

•QuantumObservations(5min)

•CellularAutomata(5min)

•QuantumCellularAutomata(10min)

• PythagorasofSamos

• PythagoreanTheorem

• Pythagoreanism

Flatland:ARomanceofManyDimensions

• EdwinAbbotAbbot (1884)• womenareline-segments• menarepolygons(n-sided)• forhecannotconceiveofanyotherexcepthimself – andplumeshimselfuponthevarietyof ItsThought asaninstanceofcreativePower.LetusleavethisGodofPointland totheignorantfruitionofhisomnipresenceandomniscience.~(theSphere)

TheQuantumMind

• Hyperspace:AScientificOdysseyThroughParallelUniverses,TimeWarps,andthe10thDimension• Michio Kako

• Human’sseein3dimensions• Noadvantagetoseeinotherdimentions• Evolutionarysurvival

• Mustourmindsworkin3dimensions?

• QuantumProbabilityinCognition• Dr.MacLennan

• TheoriesofCognition• Logic

• Aristotle’stime

• ClassicalProbability• 1970

• QuantumProbability

• CollectiveUnconscious• Jung1916

• dreams,fantasies,andotherexceptionalstatesappearnatively

• primordialimagesorarchetypes,asIhavecalledthem,belongtothebasicstockoftheunconsciouspsycheandcannotbeexplainedaspersonalacquisitions• Collectivelycalledthecollectiveunconscious

Michelangelo'sCreationofAdam

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.

CellularAutomata

• JohnvonNeumann• “Whatkindoflogicalorganizationissufficientforanautomatontoreproduceitself?”• 1903

• RegularGridofcells• Finitenumberofstatesforeachgrid• N-dimensional• Neighborhooddefinedforeachcell• Initialstatedefinedforeachcell• Achangingfunctionforeachcell• Basedonneighborhood• Usuallysameforeachcell

ProcessingImageofGameoflife

ProcessingImageofSpiernsky Triangle

GameofLife

• JohnConway1970• Infinitetwo-dimensionalorthogonalgridofcells• Twopossiblestates• Rules(functionorchangingcells)• Livingcellwithfewerthantwoliveneighbours dies• livingcellwithtwoorthreeliveneighbours liveson• Livingcellwithmorethanthreeliveneighbours dies• Deadcellwithexactlythreeliveneighbours becomesalivecell

CellularAutomata?

• TuringComplete

• EdgeofChaos

• Applicationstootherfields

Rule110:CellularAutomata

• TuringComplete• SimulateasingletapedTuringMachine• Computable

• EdgeofChaos• Lambdavalue

• 0=order• 1=chaos

01101110

Miller– UreyExperiment

• Createearlyearthconditions• methane (CH4)• water (H2O)• ammonia (NH3)• hydrogen (H2)• ContinuousElectricSparks

• AminoAcidswerecreated• Protein• 20+

QuantumCellularAutomata

• Generalizationofcellularautomata(CA)• ReversibleCA• GrössingG,ZeilingerA(1988)Quantumcellularautomata• Noagreedupondefinition

CellularAutomatavsQuantumCellularAutomata

• (CA)isa4-tuple(L,Σ,N,f) • (QCA)isa3-tuple(L,H,U)

PartitionedWatrous QCA

• Firstproofofcomputationaluniversality• GivenanyquantumTuringMachine,thereexistsaPWQCAwhichsimulatestheTuringMachinewithConstantslowdown• GivenanyPWQCA,thereexistsaTuringMachinewhichsimulatesthePWQCAwithlinearslowdown

TypesofQCA

• Reversible• LocalUnitary• 1dimensional• UniversalSimulateanyquantumcircuit• Canbesimulatedusingafamilyofquantumcircuits

• BlockPartitioned• ContinuousTime• Hamiltonian

QCAExploration• LogicalDevicesusingQCA

• QuantumDots• Xor• adder

• QuantumTuringMachinesarestilltheoretical• Confinedtoaveryfinitenumberofelements

• Opticallattices• Artificialcrystalsoflightandconsistsofmicrotraps• Crossed laser beams,

• creatingpolarizationpattern• Atomscoolandcongregateintheminima

• Resemblesacrystallattice• Quantumtunnelingcanoccur

QuantumLatticeGasAutomata

• partialdifferentialequationcanbetheevolutionofsomeCA• CAwillmimicthepartialdifferentiationequation• Continuoustimelimit• Continuousspacelimit

• QLGAhasdemonstratedtheequivalence• EvolutionofsetofquantumlatticeBoltzman equations

• Exploredtomodelphysicalsystems

QuantumTunneling

• Wave-ParticleDuality• Particle• Classicalmechanics• Sumofenergy

• Wave• Quantummechanics

QuantumTunneling• Thematterridesthewave

QuantumDotAutomata

• QuantumDots• Consistofnanoparticles• 5quantumdots• Twoelectrons

• Dotshopamongthefivestates• Electronsfindfarthestdistance

WorksCited

• Availableuponrequest