Quantum Cellular Automata...
Transcript of Quantum Cellular Automata...
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