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Unformatted text preview: I NTRODUCTION TO Q UANTUM C OMPUTING Writen by: Eleanor Rieffel and Wolfgang Polak Presented by: Anthony Luaders O UTLINE : ᶃ Introduction ᶄ Notation ᶅ Experiment ᶆ Quantum Bit ᶇ Quantum Key Distribution ᶈ Multiple Qubits ᶉ Entangled Particles ᶊ Recent News ᶋ Suggested Reading ᶌ Sources I NTRODUCTION 1980’s, Richard Feynman observed that certain quantum mechanical effects cannot be simulated on a classical computer. 1994, Peter Shor described a polynomial time quantum algorithm for factoring integers. C LASSIC C OMPUTING The time it takes to do certain computations can be decreased using parallel processors Exponential decrease in amount of time Exponential increase in the number of processors Exponential increase in the amount of physical space Q UANTUM C OMPUTING The time it takes to do certain computations can be decreased using parallel processors Exponential decrease in amount of time Linear increase in the number of processors Linear increase in the amount of physical space This is known as quantum parallelism There is a catch… While massive parallel computation can be preformed, access to the results is restricted Fix… Shor’s factorization algorithm Grover’s search algorithm O UTLINE : ᶃ Introduction ᶄ Notation ᶅ Experiment ᶆ Quantum Bit ᶇ Quantum Key Distribution ᶈ Multiple Qubits ᶉ Entangled Particles ᶊ Recent News ᶋ Suggested Reading ᶌ Sources B AR KET N OTATION The matching bra, ⟨ x, denotes the conjugate transpose of x ⟩ Example: The orthonormal basis{0 ⟩ , 1 ⟩ } can be expressed as {(1, 0) T , (0, 1) T } Any complex linear combination of 0 ⟩ and 1 ⟩ , ( a 0 ⟩ + b 1 ⟩ ), can be written ( a , b ) T Note the order of the basis vectors is arbitrary, but it must be consistent N OTATION : I NNER AND O UTER P RODUCT The inner product ⟨ xy ⟩ found by combining ⟨ x and  y ⟩ as in ⟨ x y ⟩ Example 0 ⟩ is a unit vector. ⟨ 00 ⟩ = 1 Since 0 ⟩ and 1 ⟩ are orthogonal we have ⟨ 01 ⟩ = 0 The outer product  x ⟩⟨ y  found by combining ⟨ y and  x ⟩ Example 0 ⟩⟨ 1 is the transformation that maps 1 ⟩ to 0 ⟩ 0 ⟩⟨ 1 is the transformation that maps 0 ⟩ to (0, 0) T O UTLINE : ᶃ Introduction ᶄ Notation ᶅ Experiment ᶆ Quantum Bit ᶇ Quantum Key Distribution ᶈ Multiple Qubits ᶉ Entangled Particles ᶊ Recent News ᶋ Suggested Reading ᶌ Sources E XPERIMENT Need A strong light source such as a laser pointer Three polarization filters (can be picked up at any camera supply store) Named A, B and C Polarized horizontally at 45 degrees Purpose Demonstrates some of the principles of quantum mechanics through photons and their polarization S TEP O NE Shine the laser (light source) at a projection screen Insert filter A between the laser and the screen...
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 Spring '11
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 Computer Science, Quantum computing, quantum key distribution, multiple qubits

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