Introduction to Imaginary World

発表: https://www.youtube.com/watch?v=Oxn-mgAaR7Q&t=7s

// Japanese
Goのcomplex (複素数) builtin typeについて話しました。
実用例にQuaternionとQuantum Information ScienceのDeutsch-Jozsaアルゴリズムについて話しました。GoによるDeutsch-Jozsaアルゴリズムの実装もあります。
使ったライブラリ: https://github.com/itsubaki/q

// English
I Talked about Go's complex builtin type.
As a real usage example, I picked up Quaternion and Quantum Information Science's Deutsch-Jozsa algorithm. This slide also has the implementation of Deutsch-Jozsa Algorithm in Go.
Used Library: https://github.com/itsubaki/q

Transcript

1. Introduction to Imaginary World NEW DEBUG!! ~ 転職してプログラマーになったら 一切エラーがでないんだが ~ // たふみ, DE LIKER // 2020·05·17
2. $ whoami たふみ ( @CreatorQsF ) Designer + Developer
3. $ whoami たふみ ( @CreatorQsF ) Designer + Developer
4. Go
5. Why Go? • Nice Standard Pkgs? • Clear Dependencies? • Less Syntax Sugar? • Single Binary? • Cross Compile? • Simple Syntax? • Fast Build? • gofmt?
6. No ( Actually, Definitely “Yes” )
7. Retrieved from https://golang.org/ref/spec#Types
8. Retrieved from https://golang.org/ref/spec#Types
10. Complex Number v
11. Polar Coordinates System Complex Number
12. Polar Coordinates + Complex
13. Polar Coordinates + Complex
14. Fortran real re, im complex z z = (1.0,2.0) re = real(z) ! Re im = aimag(z) ! Im end
15. Python z = 1 + 2i
16. C99 // GNU Extention #include <complex.h> ... double _Complex x = 1.0 + 2.0i; // C99 Spec #include <complex.h> ... float _Complex x = 1.0 + 2.0 * _Complex_I; Ref https://cpplover.blogspot.com/2013/11/c99.html
17. C99 // GNU Extention #include <complex.h> ... double _Complex x = 1.0 + 2.0i; // C99 Spec #include <complex.h> ... float _Complex x = 1.0 + 2.0 * _Complex_I; Ref https://cpplover.blogspot.com/2013/11/c99.html
18. Perl Ruby OCaml Haskell etc... Need to include std lib (complex is not builtin type)
19. Go package main import ( "fmt" ) func main() { z := 1 + 2i fmt.Printf("%T", z) } // output: complex128
20. Retrieved from https://github.com/golang/go/issues/19921
22. You, the people have the power - the power to create machines. The power to create happiness! You, the people, have the power to make this life free and beautiful, to make this life a wonderful adventure. Retrieved from “The Great Dictator” (1940)
23. You, the people have the power - the power to create machines. The power to create happiness! You, the people, have the power to make this life free and beautiful, to make this life a wonderful adventure. Retrieved from “The Great Dictator” (1940)
24. Let’s Make Your Life Beautiful
25. Beautiful Life ≈ Creative, Imaginary Life
26. Beautiful Life ≈ Creative, Imaginary Life
27. Usage of Complex Number • Quaternion • Quantum Information Science → Let’s aGo !
28. Quaternion 4元数
29. Quaternion
30. Quaternion This needs 3 independent complex space, so it will be lil hard to express in Go…
31. Quaternion is used for 3D Graphics rotation, like Games. Another methods: - Euler angles (オイラー角) - Rotation Matrix (回転行列) FYI
32. Euler angles (オイラー角) Euler angles needs only 3 params. ...BUT, - the computation is heavy - The problem of Gimbal Lock FYI
33. FYI Rotation Matrix (回転行列) Rotation Matrix needs 9 params ← soooo many not good for memory resources
34. Quaternion (4元数) Quaternion needs 4 params. - No Gimbal Lock - Balanced for memory & computating resources FYI
35. Quantum Information 量子情報学
36. 量子情報学入門 石坂 智 (著) 小川 朋宏 (著) 河内 亮周 (著) 木村 元 (著) 林 正人 (著) 共立出版 2012 References Retrieved from https://www.amazon.co.jp/%E9%87%8F%E5%AD%90%E6%83%85%E5%A0%B1%E7%A7%91%E5%AD%A6%E5% 85%A5%E9%96%80-%E7%9F%B3%E5%9D%82-%E6%99%BA/dp/4320122992
37. Quantum Physics Raymer, G. M. Oxford Univ. Press 2017 References Retrieved from https://www.amazon.co.jp/Quantum-Physics-What-Everyone-Needs/dp/0190250712
38. In classic Computer… A Long Time Ago, in the Galaxy Far Away...
39. 0 1 &
40. In Quantum World,
41. 0 1
42. Quantum Superposition 重ね合わせの状態
43. If all the inputs are superposition, then…?
44. - Dirac Notation - Bra-ket notation
45. Bra-ket Notation (Equation Editor++ does not support braket notation, so insteadly used \langle and \rangle.)
46. Unit Vector This is the corresponding 0, 1 to classic computing in qubit
47. Intermissions x can be anything are ugly
48. Bloch Sphere & Bloch Vector Retrieved from https://en.wikipedia.org/wiki/Bloch_ sphere
49. Unitary Evolution & Unitary Matrix * : Adjoint Matrix (随伴行列) This shows that |ψ> changes with time to |ψ>’
50. Significant Unitary Matrix • Identity Matrix • Pauli Matricies
51. Significant Unitary Matrix (cont.) • Hadamard Matrix • Also called “Hadamard Transform” when used as an operator • Particularly make the basis superposition which the probability of |0> and |1> is the same
52. Hadamard Transform
53. Hadamard Transform
54. Deutsch- Jozsa Algorithm • Multiply n+1’th bit by Pauli’s \sigma_x • Multiply all the bits by Hadamard Operator • Multiply all the bits by U_f • Multiply first n bits by Hadamard Operator • If the observed classical first n bit array is 0...0, then it is constant function, otherwise balanced function.
55. Deutsch- Jozsa Algorithm (cont.) • f is Oracle, it is like black box • So in classical computing, 2/n + 1 inputs must be evaluated. → must be asked 2^(n-1) + 1 times • Deutsch-Jozsa needs 1 time ask
56. Deutsch- Jozsa Algorithm (cont.)
57. Retrieved from https://github.com/itsubaki/q
58. Deutsch- Jozsa Impl package main import ( "fmt" qsim "github.com/itsubaki/q" )
59. Deutsch- Jozsa Impl // deutschjozsa return is given f is constant, returns true. Otherwise retuens false. func deutschjozsa(size int, f func(_ *qsim.Q, _ ...qsim.Qubit)) string { q := qsim.New() is := make([]qsim.Qubit, size) for i := range is { is[i] = q.Zero() } o := q.One() // equivalent to `o := q.Zero(); q.X(o);` q.H(is...) q.H(o) // Apply func as Oracle Uf f(q, is...) q.H(is...) q.Measure(is...) return q.Binary() }
60. Deutsch- Jozsa Impl func constant(_ *qsim.Q, _ ...qsim.Qubit) { }
61. func balanced(space *qsim.Q, qs ...qsim.Qubit) { cnt := 0 for _, q := range qs { if cnt%2 == 0 { space.Z(q) } cnt++ } } Deutsch- Jozsa Impl
62. Deutsch- Jozsa Impl func main() { fmt.Println("balanced: ", deutschjozsa(8, balanced)) fmt.Println("constant: ", deutschjozsa(8, constant)) }
63. Deutsch- Jozsa Impl deutsch-jozsa $ make go run main.go balanced: 101010101 constant: 000000000
65. Introduction to Imaginary World NEW DEBUG!! ~ 転職してプログラマーになったら 一切エラーがでないんだが ~ // たふみ, DE LIKER // 2020·05·17 Follow me on Twitter → @CreatorQsF