量子類神經元網路 簡介與應用ppt课件

1、Quantum Neural NetworksIntroduction & Applications虞台文ContentlIntroductionlThe Qtron NN ModellSolving Problems Using Qtron NNslApplicationslDetail of Visual CryptographylConclusionsQuantum Neural NetworksIntroduction & ApplicationsIntroduction想當年，也曾意氣風發Life from the cradle to the gravelPastl八

2、字、運勢lNothing can be done? lPresentl創造佳績lHow?lFuturel卡奴l邁向顛峰趨吉避凶往事只堪成追憶Life from the cradle to the gravelPastl八字、運勢lNothing can be done? lPresentl創造愉快生活lHow?lFuturel卡奴l邁向顛峰趨吉避凶往事只堪成追憶Life from the cradle to the gravelPastl八字、運勢lNothing can be done? lPresentl創造愉快生活lHow?lFuturel卡奴l邁向顛峰趨吉避凶往事只堪成追憶?Life

3、from the cradle to the gravelPastl八字、運勢lNothing can be done? lPresentl創造愉快生活lHow?lFuturel卡奴l邁向顛峰往事只堪成追憶趨吉避凶繼往開來Exploitation + ExplorationThe PhysicsGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumGoal:PastGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOpti

4、mum(八字、運勢)Goal:PresentGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimum(八字、運勢)Goal:PresentGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimum趨吉避凶renders us to be stuck at a local optimum.Goal:PresentGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalO

5、ptimumLocalOptimum趨吉避凶Exploitation + Explorationrenders us to be stuck at a local optimum.Goal:PresentGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimum趨吉避凶Goal:Exploitation + ExplorationPastPresentFutureGlobalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimumLocalOptimum

6、Goal:Exploitation + ExplorationSolving Problems by Physics為天地立心為生民立命為往聖繼絕學為萬世開太平Exploitation + ExplorationNewtons LawUncertaintyPrincipleEnergy goes low always.We live in a probability world.Solving Problems by Physics為天地立心為生民立命為往聖繼絕學為萬世開太平Exploitation + ExplorationNewtons LawUncertaintyPrincipleEne

7、rgy goes low always.We live in a probability world.見山有時不是山見水有時不是水可邁向顛峰也 見山是山 見水是水可趨吉避凶也How?天將降大任於斯人也，必先苦其心志，勞其筋骨， 餓其體膚，空乏其身行，行拂亂其所為，所以動心忍性，曾益其所不能。 Quantum Neural NetworksIntroduction & ApplicationsThe Qtron NN ModelThe Qtroni(ai ). . .0 1 2qi1aiQiActive valueQi0, 1, , qi1IiRExternal Stimulus()ij

8、jjjT a QInternal StimulusNiNoiseQuantum NeuronThe Qtroni(ai ). . .0 1 2qi1aiQiActive valueQi0, 1, , qi1IiRExternal Stimulus()ijjjjT a QInternal StimulusNiNoiseFree-Mode QtronThe Qtroni(ai ). . .0 1 2qi1aiQiActive valueQi0, 1, , qi1IiRExternal Stimulus()ijjjjT a QInternal StimulusNiNoiseClamp-Mode Qt

9、ronInput StimulusInternalStimulusExternalStimulusNoiseNoiseFreeTermi(ai ). . .NoiseLevel TransitionRunning Asynchronouslyi(ai ). . .Energy FunctionInteractionAmong QtronsInteractionwithExternal StimuliConstantMonotonically NonincreasingMonotonically Nonincreasing趨吉避凶The Qtron NNInterface/Hidden Qtro

10、ns clamp-modefree-modefree mode Hidden Qtrons Interface QtronsPersistent Noise-Injection Mechanism clamp-modefree-modefree mode Hidden Qtrons Interface QtronsNoises dont have holiday.Question-AnsweringFeed a question by clamping some interface Qtrons. clamp-modefree-modefree mode Hidden Qtrons Inter

11、face QtronsQuestion-AnsweringGet the answer when the NN settles down. clamp-modefree-modefree mode Hidden Qtrons Interface QtronsBounded Noise Spectrai(ai ). . .NiNoise,iiiNNNMostNegativeMostPositiveiNiN0The noise strength for simulated annealing is possibly unbounded unless the temperature reaches

12、zero.Know-Energy Systems 知能Know-Energy Systems 知能Never occurFeatureA Qtron NN can settle down iff its energy is almost lost.The solution reported by the Qtron NN must be very good.Quantum Neural NetworksIntroduction & ApplicationsSolving Problems Using Qtron NNsExample: Adder1 25 + 7=5 + 7=1 25

13、+ 7=1 25 + 7=1 2 How do you solve these problems? How about this?3 5Example: Adder1 25 + 7=5 + 7=1 25 + 7=1 25 + 7=1 2 How do you solve these problems? How about this?3 5I bet that you solve the problem by energy minimization.It appears as a memory association process of human being.Associative Memo

14、riesProvide the known information to get the unknown information.The Associative Adder543654+XY+Z1719The Associative Adder5 4 36 5 4+171 95 4 36 5 4+171 95 4 36 5 4+171 95 4 36 5 4+171 95 4 36 5 4+171 95 4 36 5 4+171 9The Associative Adder5 4 36 5 4+171 95 4 36 5 4+171 95 4 36 5 4+171 91 4 36 5 4+07

15、7 95 4 36 5 4+171 91 2 39 8 8+111 1Qtron NN Implementation 3-Digit Associative Adder 2XQ1XQ0XQ2YQ1YQ0YQ2ZQ1ZQ0ZQ3ZQ+addend1addend2sumXYZ*0,1,9iQ Qtron NN Implementation 3-Digit Associative Adder 2XQ1XQ0XQ2YQ1YQ0YQ2ZQ1ZQ0ZQ3ZQ+100101102103 Weights of digits 2010iXiiXQ2010jYijYQ3010kZikZQQtron NN Impl

16、ementation 3-Digit Associative Adder 2XQ1XQ0XQ2YQ1YQ0YQ2ZQ1ZQ0ZQ3ZQ+2010iXiiXQ2010jYijYQ200202110010iXjYiiijkZikQQQGoal:XYZ3010kZikZQQtron NN Implementation 3-Digit Associative Adder 200202110010iXjYiiijkZikQQQGoal:220022011101020iXjYadderiikZikijQQQEMinimizeQtron NN Implementation 3-Digit Associati

17、ve Adder 220022011101020iXjYadderiikZikijQQQEMinimize0The energy value of a solution state.“知能Quantum Neural NetworksIntroduction & ApplicationsApplicationsDemonstrationslN-Queen SolverlSudoku (數獨)lVisual CryptographyThe N-Queen SolverA bench mark of constraint satisfaction problem.The N-Queen S

18、olver01000000000001001000000000000010000100000000000100100000000010000,1ijQ Facts0100000000000100100000000000001000010000000000010010000000001000lEach row and column sum to one.lEach diagonal sums to zero or one.SkipMath0,1ijQ N-Queen as an Integer Programfor rowsfor columnsfor diagonals for diagona

19、ls /lEach row and column sum to one.lEach diagonal sums to zero or one.constraintN-Queen as an Integer Programfor rowsfor columnsfor diagonals for diagonals /lEach row and column sum to one.lEach diagonal sums to zero or one.constraintTo build a known-energy system, inequalities have to be converted

20、 to equalities.N-Queen as an Integer Programfor rowsfor columnsfor diagonals for diagonals /lEach row and column sum to one.lEach diagonal sums to zero or one.constraintSlack variables added.They serve as hidden QtronsEnergy Functionfor the N-Queen SolverKnow-Energy Propertyfor the N-Queen Solvermus

21、t be zeromust be zeromust be zeromust be zeroMust be zeroKnow-Energy Propertyfor the N-Queen Solvermust be zeromust be zeromust be zeromust be zeroMust be zeroSee the paper for the details.The Operating Scenariofor the N-Queen SolverThe Operating Scenariofor the N-Queen SolverThe Operating Scenariof

22、or the N-Queen SolverLocal-Minimafor the N-Queen SolverThey are local-minima, and all are infeasible.SudokuSudokuA reasonable puzzle must have a unique solution.ProblemslHow to resolve a puzzle?lHow to generate a puzzle?lEnsure uniquenesslHow to control the level of difficulty?Qtron NN provides a to

23、tal solution. Visual Cryptography志明：妳甘有影是春嬌志明：妳甘有影是春嬌?志明：妳甘有影是春嬌志明：妳甘有影是春嬌?志明：妳甘有影是春嬌志明：妳甘有影是春嬌?志明：妳甘有影是春嬌志明：妳甘有影是春嬌?What is Visual Cryptography?lVisual Cryptography (VC)lEncrypts secrete into a set of images (shares).lDecrypts secrete using eyes.lApplications:lIdentificationlAuthorizationlSemipubli

24、c EncryptionlKey ManagementlEntertainment . . .Share 2Share 1Secrete ImageWhat is Visual Cryptography?lVisual Cryptography (VC)lEncrypts secrete into a set of images (shares).lDecrypts secrete using eyes.lApplications:lIdentificationlAuthorizationlSemipublic EncryptionlKey ManagementlEntertainment .

25、 . .Example: (2, 2)Target imageShare image2Share image1Plane shares are usedTraditional ApproacheslNaor and Shamir (2,2)PixelProbabilityShares#1 #2Superposition ofthe two shares5 . 0p5 . 0p5 . 0p5 . 0pWhitePixelsBlackPixelsThe Code BookTraditional ApproacheslNaor and Shamir (2,2)PixelProbabilityShar

26、es#1 #2Superposition ofthe two shares5 . 0p5 . 0p5 . 0p5 . 0pWhitePixelsBlackPixelsThe Code BookComplex Access SchemesQtron NN ApproachThe VA Schemekeyshareuser shares(resource 2)user shares(resource 1)stackingstackingVIPIPPVIPIPPVery Important Person.Key ShareUser ShareUser ShareUser ShareVIPIPPDem

27、oThe SE SchemeThe database of AIMM labUser KeyJanetABJennyCDHsunliXYBillUVpublic share(database of AIMM lab)ABCDXYUVstackingusershareskeysJanetThe SE SchemeJennyHsunliBillstackingJanetJennyHsunliBillExperimental Resultpublic share(database of AIMM lab)usershareskeysFull Access Scheme 3 Shares朝朝 辭辭 白

28、白帝帝彩彩雲雲間間SharesFull Access Scheme 3 Shares朝朝 辭辭 白白帝帝彩彩雲雲間間SharesTheoretically, unrealizable.Theoretically, unrealizable.We did it in practical sense. We did it in practical sense. Full Access Scheme 3 SharesS1S2S3S1+S2S1+S3S2+S3S1+S2+S3Access Schemewith Forbidden Subset(s)Anyone knows what it is?Acc

29、ess Schemewith Forbidden Subset(s)人人 之之 初初性性本本X善善Theoretically, realizable.Theoretically, realizable.SharesAccess Schemewith Forbidden Subset(s)S1S2S3S1+S2S1+S3S2+S3S1+S2+S3Quantum Neural NetworksIntroduction & ApplicationsDetail ofVisual CryptographySkipEnergy Function for VCVisual Cryptography

30、Image HalftoningImage Stacking+Image HalftoningGraytone ImageHalftoning0255Halftone Image0 (Transparent)1Graytone image halftone image can be formulated as to minimize the energy function of a Qtron NN.Image HalftoningGraytone ImageHalftoning0255Halftone Image0 (Transparent)1Graytone image halftone

31、image can be formulated as to minimize the energy function of a Qtron NN.In ideal case, each pair of corresponding small areas has the same average graylevel. The Qtron NN for Image HalftoningPlane-G (Graytone image)Plane-H (Halftone image)Image HalftoningHalftoningClamp-modeFree-modePlane-G (Grayto

32、ne image)Plane-H (Halftone image)QuestionAnswerImage RestorationPlane-G (Graytone image)Plane-H (Halftone image)RestorationClamp-modeFree-modeQuestionAnswerStacking Rule+The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Qtron NN.Stacking Rule+The satisf

33、action of stacking rule can also be formulated as to minimize the energy function of a Qtron NN.+=s1s2hStacking Rule+The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Qtron NN.The energy function for the stacking rule.See the paper for the detail. The T

34、otal Energy+Share 1TargetShare 1Share 2TargetShare 2TotalEnergyImage HalftoningStacking RuleThe Qtron NN for VC/VAPlane-GS1Plane-HS1Public SharePlane-HS2Plane-GS2User SharePlane-GTPlane-HTKeyclampclampclampCD XY UVApplication Visual CryptographyPlane-GS1Plane-HS1Share 1Plane-HS2Plane-GS2Share 2Plane

35、-GTPlane-HTTargetClamp-ModeClamp-ModeClamp-ModeFree-ModeFree-ModeFree-ModeApplication Visual CryptographyPlane-GS1Plane-HS1Share 1Plane-HS2Plane-GS2Share 2Plane-GTPlane-HTTargetClamp-ModeClamp-ModeClamp-ModeFree-ModeFree-ModeFree-ModeApplication Visual AuthorizationPlane-GS1Plane-HS1User ShareAuthorityAuthorityPlane-HS2Plane-GS2Plane-GTPlane-HTKey ShareKey ShareUser ShareVIPIPPApplication Visual A