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? © 2009- TopeconHeroes
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• • • = ℎ ℎ
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• • • 0 = 1 0 1 = 0 1 • 2
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• = 0 0 + 1 1 • 2 • 2 −1 =0 = 1 • = 1 2 0 + 1 2 1 0 1 • 0 1
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• = 1 2 00 + 01 + 10 + 11 = 1 2 00 + 10 + 1 2 11 • 00 = 0 ⊗ 0 •
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= 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
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• • 0 0 + 1 1 → 0 ′ 0 + 1 ′ 1 0 1 = 0 ′ 1 ′ •
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• • • • • = 1 2 1 1 1 −1
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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
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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
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• • • 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
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= 1 2 0 + 1 ∶ = 0 ∶ = 1 2 0 0 + 1 0 ′ = 1 2 0 + 1 ′ = 1 2 0 0 + 1 1
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• = 1 2 0 0 + 1 0 • ′ = 1 2 0 0 + 1 1 • • ′
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H H | a 0 > | b 0 > | c 0 > | c 1 >
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• 1 0 1 + 1 = 1 = 1 0 1 = 1100 0 1 = 1101 •
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• 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 •
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• • • • 2 → •
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• • • 2100 = 1.26765 × 1030 2014 257885161 − 1 1742
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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 •
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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 }
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