1. Quantum Neural Networks Introduction & Applications 虞台文

2. Content Introduction The Q’tron NN Model Solving Problems Using Q’tron NN’s Applications Detail of Visual Cryptography Conclusions

3. Quantum Neural Networks Introduction & Applications Introduction 想當年，也曾意氣風發

4. Life  from the cradle to the grave Past – 八字、運勢 – Nothing can be done? Present – 創造佳績 – How? Future – 卡奴 – 邁向顛峰 趨吉避凶 往事只堪成追憶

5. Life  from the cradle to the grave Past – 八字、運勢 – Nothing can be done? Present – 創造美好生活 – How? Future – 卡奴 – 邁向顛峰 趨吉避凶 往事只堪成追憶

6. Life  from the cradle to the grave Past –八–八字、運勢 –N–Nothing can be done? Present –創–創造美好生活 –H–How? Future –卡–卡奴 –邁–邁向顛峰 趨吉避凶 往事只堪成追憶 ?

7. Life  from the cradle to the grave Past – 八字、運勢 – Nothing can be done? Present – 創造美好生活 – How? Future – 卡奴 – 邁向顛峰 往事只堪成追憶 趨吉避凶 繼往開來 Exploitation + Exploration

8. The Physics Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum Goal:

9. Past Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum ( 八字、運勢 ) Goal:

10. Present Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum ( 八字、運勢 ) Goal:

11. Present Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum 趨吉避凶 renders us to be stuck at a local optimum. Goal:

12. Present Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum 趨吉避凶 Exploitation + Exploration renders us to be stuck at a local optimum. Goal:

13. Present Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum 趨吉避凶 Goal: Exploitation + Exploration

14. Past  Present  Future Global Optimum Local Optimum Local Optimum Local Optimum Local Optimum Local Optimum Goal: Exploitation + Exploration

15. Solving Problems by Physics Exploitation + Exploration Newton’s Law Uncertainty Principle Energy goes low always. We live in a probability world.

16. Solving Problems by Physics Exploitation + Exploration Newton’s Law Uncertainty Principle Energy goes low always. We live in a probability world. 見山有時不是山 見水有時不是水 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 見山是山 見水是水 可趨吉避凶也

17. How?

18. Quantum Neural Networks Introduction & Applications The Q’tron NN Model

19. The Q’tron  i (a i )  i (a i )... 012 qi1qi1 aiQiaiQi Active value Q i  {0, 1, …, q i  1} IiRIiR External Stimulus Internal Stimulus NiNi Noise Quantum Neuron

20. The Q’tron  i (a i )  i (a i )... 012 qi1qi1 aiQiaiQi Active value Q i  {0, 1, …, q i  1} IiRIiR External Stimulus Internal Stimulus NiNi Noise Free-Mode Q’tron

21. The Q’tron  i (a i )  i (a i )... 012 qi1qi1 aiQiaiQi Active value Q i  {0, 1, …, q i  1} IiRIiR External Stimulus Internal Stimulus NiNi Noise Clamp-Mode Q’tron

22. Input Stimulus Internal Stimulus ExternalStimulus Noise Free Term  i (a i )  i (a i )... Noise

23. Level Transition Running Asynchronously  i (a i )  i (a i )...

24. Energy Function Interaction Among Q’trons Interaction with External Stimuli Constant Monotonically Nonincreasing 趨吉避凶

25. The Q’tron NN

26. Interface/Hidden Q’trons clamp-mode free-mode free mode  Hidden Q’trons Interface Q’trons

27. Persistent Noise-Injection Mechanism clamp-mode free-mode free mode  Hidden Q’trons Interface Q’trons Noises don’t have holiday.

28. Question-Answering Feed a question by clamping some interface Q’trons. clamp-mode free-mode free mode  Hidden Q’trons Interface Q’trons

29. Question-Answering Get the answer when the NN settles down. clamp-mode free-mode free mode  Hidden Q’trons Interface Q’trons

30. Bounded Noise Spectra  i (a i )  i (a i )... NiNi Noise Most Negative Most Positive 0 The noise strength for simulated annealing is possibly unbounded unless the temperature reaches zero.

31. Know-Energy Systems 知能

32. Know-Energy Systems 知能 Never occur

33. Feature A Q’tron NN can settle down iff its energy is almost lost. The solution reported by the Q’tron NN must be very good.

34. Quantum Neural Networks Introduction & Applications Solving Problems Using Q’tron NN’s

35. Example: Adder 1 2 5+ 7 = 5+ 7 = 1 2 5+ 7 = 1 2 5+ 7 = 1 2 How do you solve these problems? How about this? 35

36. Example: Adder 1 2 5+ 7 = 5+ 7 = 1 2 5+ 7 = 1 2 5+ 7 = 1 2 How do you solve these problems? How about this? 35 I bet that you solve the problem by energy minimization. It appears as a memory association process of human being.

37. Associative Memories Provide the known information to get the unknown information.

38. The Associative Adder 543 654+ X Y+ Z 1719

39. 543 654+ 1719 543 654+ 1719 543 654+ 1719 543 654+ 1719 543 654+ 1719 543 654+ 1719

40. 543 654+ 1719 543 654+ 1719 543 654+ 1719 143 654+ 0779 543 654+ 1719 123 988+ 1111

41. Q’tron NN Implementation  3-Digit Associative Adder + addend 1 addend 2 sum X Y Z

42. Q’tron NN Implementation  3-Digit Associative Adder + 10 0 10 1 10 2 10 3  Weights of digits

43. Q’tron NN Implementation  3-Digit Associative Adder + Goal: XYZ

44. Q’tron NN Implementation  3-Digit Associative Adder Goal: Minimize

45. Q’tron NN Implementation  3-Digit Associative Adder Minimize 0 The energy value of a solution state. “ 知能 ”

46. Quantum Neural Networks Introduction & Applications Applications

47. Demonstrations N-Queen Solver Sudoku ( 數獨 ) Visual Cryptography

48. The N-Queen Solver A bench mark of constraint satisfaction problem.

49. The N-Queen Solver 0 1 000000 00000 1 00 1 0000000 000000 1 0 000 1 0000 0000000 1 00 1 00000 0000 1 000

50. Facts 0 1 000000 00000 1 00 1 0000000 000000 1 0 000 1 0000 0000000 1 00 1 00000 0000 1 000 1. Each row and column sum to one. 2. Each diagonal sums to zero or one. Skip Math

51. N-Queen as an Integer Program for rows for columns for diagonals \ for diagonals / 1. Each row and column sum to one. 2. Each diagonal sums to zero or one. constraint

52. N-Queen as an Integer Program for rows for columns for diagonals \ for diagonals / 1. Each row and column sum to one. 2. Each diagonal sums to zero or one. constraint To build a known-energy system, inequalities have to be converted to equalities.

53. N-Queen as an Integer Program for rows for columns for diagonals \ for diagonals / 1. Each row and column sum to one. 2. Each diagonal sums to zero or one. constraint Slack variables added. They serve as hidden Q’trons Slack variables added. They serve as hidden Q’trons

54. Energy Function for the N-Queen Solver

55. Know-Energy Property for the N-Queen Solver must be zero Must be zero

56. Know-Energy Property for the N-Queen Solver must be zero Must be zero See the paper for the details.

57. The Operating Scenario for the N-Queen Solver

59. Demo

60. Local-Minima for the N-Queen Solver They are local-minima, and all are infeasible.

61. Sudoku

62. A reasonable puzzle must have a unique solution.

63. Problems How to resolve a puzzle? How to generate a puzzle? – Ensure uniqueness How to control the level of difficulty? Q’tron NN provides a total solution. Demo

64. Visual Cryptography

65. 志明：妳甘有影是春嬌 ???

69. What is Visual Cryptography? Visual Cryptography (VC) – Encrypts secrete into a set of images (shares). – Decrypts secrete using eyes. Applications: – Identification – Authorization – Semipublic Encryption – Key Management – Entertainment... Share 2Share 1 Secrete Image

70. What is Visual Cryptography? Visual Cryptography (VC) – Encrypts secrete into a set of images (shares). – Decrypts secrete using eyes. Applications: – Identification – Authorization – Semipublic Encryption – Key Management – Entertainment...

71. Example: (2, 2) Target image Share image2 Share image1 Plane shares are used

72. Traditional Approaches Naor and Shamir (2,2) PixelProbability Shares #1 #2 Superposition of the two shares White Pixels Black Pixels The Code Book

73. Traditional Approaches Naor and Shamir (2,2) PixelProbability Shares #1 #2 Superposition of the two shares White Pixels Black Pixels The Code Book Complex Access Schemes 

74. Q’tron NN Approach

75. The VA Scheme key share user shares (resource 2) user shares (resource 1) stacking … … VIP IP P … VIP IP P V ery I mportant P erson. …

76. Key Share User Share VIP IP P Demo

77. The SE Scheme The database of AIMM lab User Key JanetAB JennyCD HsunliXY BillUV The database of AIMM lab User Key JanetAB JennyCD HsunliXY BillUV

78. public share (database of AIMM lab) ABCDXYUV stacking user shares keys Janet The SE Scheme JennyHsunliBill

79. stacking Janet Jenny HsunliBill Experimental Result public share (database of AIMM lab) user shares keys

80. Full Access Scheme  3 Shares 朝 辭 白 帝 彩 雲 間 Shares

81. Full Access Scheme  3 Shares 朝 辭 白 帝 彩 雲 間 Shares Theoretically, unrealizable. We did it in practical sense. Theoretically, unrealizable. We did it in practical sense.

82. Full Access Scheme  3 Shares S1S2S3 S1+S2S1+S3S2+S3S1+S2+S3

83. Access Scheme with Forbidden Subset(s) Anyone knows what it is?

84. Access Scheme with Forbidden Subset(s) 人 之 初 性 本 X 善 Theoretically, realizable. Shares

85. Access Scheme with Forbidden Subset(s) S1S2S3 S1+S2S1+S3S2+S3S1+S2+S3

86. Quantum Neural Networks Introduction & Applications Detail of Visual Cryptography Skip

87. Energy Function for VC Visual Cryptography Image Halftoning Image Stacking +

88. Image Halftoning Graytone Image Halftoning 0 255 Halftone Image 0 (Transparent) 1 Graytone image  halftone image can be formulated as to minimize the energy function of a Q’tron NN.

89. Image Halftoning Graytone Image Halftoning 0 255 Halftone Image 0 (Transparent) 1 Graytone image  halftone image can be formulated as to minimize the energy function of a Q’tron NN. In ideal case, each pair of corresponding small areas has the `same’ average graylevel.

90. The Q’tron NN for Image Halftoning Plane- G (Graytone image) Plane- H (Halftone image)

91. Image Halftoning Halftoning Clamp-mode Free-mode Plane- G (Graytone image) Plane- H (Halftone image) Question Answer

92. Image Restoration Plane- G (Graytone image) Plane- H (Halftone image) Restoration Clamp-mode Free-mode Question Answer

93. Stacking Rule ++++ The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN.

94. Stacking Rule ++++ The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN. + = s1s1 s2s2 h

95. Stacking Rule ++++ The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN. The energy function for the stacking rule. See the paper for the detail.

96. The Total Energy + Share 1 Target Share 1 Share 2 TargetShare 2 Total Energy Image Halftoning Stacking Rule

97. The Q’tron NN for VC/VA Plane-GS1 Plane-HS1 Public Share Plane-HS2 Plane-GS2 User Share Plane-GT Plane-HT Key clamp CDXYUV

98. Application  Visual Cryptography Plane-GS1 Plane-HS1 Share 1 Plane-HS2 Plane-GS2 Share 2 Plane-GT Plane-HT Target Clamp-Mode Free-Mode

99. Application  Visual Cryptography Plane-GS1 Plane-HS1 Share 1 Plane-HS2 Plane-GS2 Share 2 Plane-GT Plane-HT Target Clamp-Mode Free-Mode

100. Application  Visual Authorization Plane-GS1 Plane-HS1 User Share Authority Plane-HS2 Plane-GS2 Plane-GT Plane-HT Key Share User Share VIPIPP

101. Application  Visual Authorization Plane-GS1 Plane-HS1 User Share Authority Clamp-Mode Free-Mode Plane-HS2 Plane-GS2 Clamp-Mode Free-Mode Plane-GT Plane-HT Clamp-Mode Free-Mode Key Share User Share VIPIPP Producing key Share & the first user share.

102. Application  Visual Authorization Plane-GS1 Plane-HS1 User Share Authority Clamp-Mode Plane-HS2 Plane-GS2 Clamp-Mode Free-Mode Plane-GT Plane-HT Clamp-Mode Some are clamped and some are free. Key Share User Share VIPIPP Producing other user shares.

103. Application  Visual Authorization Plane-GS1 Plane-HS1 User Share Authority Clamp-Mode Plane-HS2 Plane-GS2 Clamp-Mode Free-Mode Plane-GT Plane-HT Clamp-Mode Some are clamped and some are free. Key Share User Share VIPIPP Producing other user shares.

104. Application  Visual Authorization Plane-GS1 Plane-HS1 User Share Authority Clamp-Mode Plane-HS2 Plane-GS2 Clamp-Mode Free-Mode Plane-GT Plane-HT Clamp-Mode Some are clamped and some are free. Key Share User Share VIPIPP

105. Key Share User Share VIP IP P

106. Quantum Neural Networks Introduction & Applications Conclusions

107. Features of Q’tron NN Solving Problems by Physics Local-Minima Free Auto-Reversibility Associativity Question-Answering 知能