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Quantum Computation
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N@N
March 09, 2014
Technology
0
270
Quantum Computation
カーネル/VM探検隊@関西 6で発表した内容です.
※追記:特にアルゴリズムなどにいくつか誤りが含まれています(時間等の都合で訂正の予定は今の所なし).
N@N
March 09, 2014
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Transcript
None
• • • • • •
• • • • •
? © 2009- TopeconHeroes
• • • •
• • • = ℎ ℎ
• •
• • •
• • • •
• •
• • • • •
• • •
• • •
• • •
• • • 0 = 1 0 1 =
0 1 • 2
• = 0 0 + 1 1 • 2 •
2 −1 =0 = 1 • = 1 2 0 + 1 2 1 0 1 • 0 1
• = 1 2 00 + 01 + 10 +
11 = 1 2 00 + 10 + 1 2 11 • 00 = 0 ⊗ 0 •
= 1 2 0 + 1 2 1 ⊗ ⊗
⋯ ⊗ = 1 2 0 + 1 2 1 = 1 2 2 0 ⊗ 0 ⊗ ⋯ ⊗ 0 + ⋯ + 1 ⊗ 1 ⊗ ⋯ ⊗ 1 = 1 2 2 00 ⋯ 0 + ⋯ + 11 ⋯ 1 • 2
• 2
• • •
None
• • 0 0 + 1 1 → 0 ′
0 + 1 ′ 1 0 1 = 0 ′ 1 ′ •
• • • • • = 1 2 1 1
1 −1
0 = 1 2 1 1 1 −1 1 0
= 1 2 0 + 1 1 2 0 + 1 = 1 2 1 1 1 −1 1 2 0 + 1 = 1 2 1 1 1 −1 1 0 + 0 1 = 1 2 1 1 1 −1 1 1 = 1 2 2 0 = 1 0 = 0
1 = 1 2 1 1 1 −1 0 1
= 1 2 0 − 1 1 2 0 − 1 = 1 2 1 1 1 −1 1 2 0 − 1 = 1 2 1 1 1 −1 1 0 + 0 −1 = 1 2 1 1 1 −1 1 −1 = 1 2 0 2 = 0 1 = 1
• • • 1 = 1 0 0 1 0
0 0 0 0 0 0 0 0 1 1 0 = ⨁ ′ ′ a ′ ′ 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0
= 1 2 0 + 1 ∶ = 0 ∶
= 1 2 0 0 + 1 0 ′ = 1 2 0 + 1 ′ = 1 2 0 0 + 1 1
• = 1 2 0 0 + 1 0 •
′ = 1 2 0 0 + 1 1 • • ′
• •
• •
H H | a 0 > | b 0 >
| c 0 > | c 1 >
• 1 0 1 + 1 = 1 = 1
0 1 = 1100 0 1 = 1101 •
• 0 1 = 1 1 0 0 + 1
2 0 1 + 1 3 1 0 + 1 4 1 1 0 1 = 0000 + 0100 + 1000 + 1100 0 1 = 0000 + 0110 + 1010 + 1101 •
• •
• • • • 2 → •
• •
• • •
• • • •
• • • 2100 = 1.26765 × 1030 2014 257885161
− 1 1742
• • • •
•
• •
qureg x1[2]; // 2-qubit quantum register x1 qureg x2[2]; //
2-qubit quantum register x2 H(x1); // Hadamard operation on x1 H(x2[1]); // Hadamard operation on the first qubit of the register x2 •
operator diffuse (qureg q) { H(q); // Hadamard Transform Not(q);
// Invert q CPhase(pi, q); // Rotate if q=1111.. !Not(q); // undo inversion !H(q); // undo Hadamard Transform }
None
None
None
• •
None
•
None
• •
• • •
None
None
None
• • •