Presentation is loading. Please wait.

Presentation is loading. Please wait.

McKay Graybill.  They already exist  Different models and ideas  Quantum Parallelism  Measurement is tricky, inherently imprecise.

Similar presentations


Presentation on theme: "McKay Graybill.  They already exist  Different models and ideas  Quantum Parallelism  Measurement is tricky, inherently imprecise."— Presentation transcript:

1 McKay Graybill

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

3

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

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

6  “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

7  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

8  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

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

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

11  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


Download ppt "McKay Graybill.  They already exist  Different models and ideas  Quantum Parallelism  Measurement is tricky, inherently imprecise."

Similar presentations


Ads by Google