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Classical Computation – Bits |
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Bits represented by a two level system: 0 and 1 |
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Each bit is either 0 or 1 |
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Quantum Computation – Quantum Bits or “Qubits” |
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Qubits represented by a two level system: |`ñ and |¯ñ |
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Each bit is either |`ñ or |¯ñ |
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Ions |
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Hyperfine ground states of 111Cd+
(|`ñ and |¯ñ) |
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Qubit rotations via microwaves |
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Quantum memory |
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Photons |
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Two orthogonal polarizations (|Hñ and |Vñ) |
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Qubit rotations with l/2 plate |
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Quantum communication |
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“Flying Qubit” |
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“Inseparability of the wave function” |
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(|Hñ + |Vñ) * (|`ñ + |¯ñ) separable |
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(|Hñ|`ñ + |Vñ|¯ñ) inseparable |
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Separable case: Measurement of the photon state
tells you nothing about the state of the ion. |
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Inseparable case: Measurement of the photon
state collapses the ion state. |
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|Hñ: ion à |`ñ and |Vñ: ion à |¯ñ |
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Allows for parallel computation |
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Evaluation of a function f(x) for many different
values of x simultaneously |
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Fundamental feature of many quantum algorithms |
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Shor’s (1994) factoring algorithm |
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Grover’s (1995) search algorithm |
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Quantum communication |
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Provably secure information transfer |
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Dense coding |
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Entangled state: |yñentangled =
|Hñ|`ñ + |Vñ|¯ñ |
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Mixed state: |yñmixed
= |
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To prove entanglement, must perform experiment
in a rotated basis. Why? |
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Both would give same result for unrotated basis
experiment. |
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Notes