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McKay Graybill

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They already exist Different models and ideas Quantum Parallelism Measurement is tricky, inherently imprecise

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Represented by a unitary matrix ◦ Controlled-Not ◦ Controlled-Controlled-Not (Toffoli) ◦ Hadamard

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Can simulate any combination of gates Example (Steane, 1998): C NOT =

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“Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer”, 1994 ◦ Inspired by the work of Dan Simon, Computations are dependent upon physics Finding the period of a function

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M, a, m ∈ ℤ : M 2 < 2 m < 2M 2 Qubits required: m + ⌈log 2 (M)⌉ f(x) = a x mod M, for all 0 < x < 2 m – 1 ◦ Measure the state to align amplitude function Fourier transform, Euclidean verification, repeat as necessary

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O(√n) search on unsorted dataset of size n Requires N + 1 qubits, where 2 N ≥ n ◦ Extra qubit is Boolean result of test function P(x) Custom transformation Repeat transformations to increase reading state where P(x) is true

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Truly Random Number Generation Data Key Distribution and Truly Secure Communication Constraint Satisfaction Problems Simulation of actual physical environments Probably more…

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Error threshold Scalability Specialized ◦ Math and Physics is still the API Shor’s 2003 Paper

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Doug Applegate BACON, D., AND VAN DAM, W Recent progress in quantum algorithms. Communications of the ACM, Vol. 53, No. 2, CHANG, K I.B.M. researchers inch toward quantum computer. The New York Times. CORLEY, A Quantum chip helps crack code. IEEE Spectrum. FEYNMANN, R. P Quantum mechanical computers. Foundations of Physics, Vol. 16, No. 6. GROVER, L. K A fast, quantum mechanical algorithm for database search. ph/ v3. GUIZZO, E Loser: D-Wave does not quantum compute. IEEE Spectrum. RIEFFEL, E., AND POLAK, W An introduction to quantum computing for non-physicists. ACM Computing Surveys Volume 32 Issue 3, SHOR, P. W Polynomial-time Algorithms for Prime-factorization and Discrete Logarithms on a Quantum Computer. SHOR, P Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SHOR, P Why haven’t more quantum algorithms been found? Journal of the ACM Vol. 50 Issue 1, STEANE, A Quantum computing. Rep. Prog. Phys.Vol. 61, No. 2, 171. VAN METER, R., AND OSKIN, M Architectural implications on quantum computing technologies. ACM Journal on Emerging Technology in Computing Systems Vol. 2 No

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