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Wave-Particle Duality and Simple Quantum Algorithms

Wave-Particle Duality and Simple Quantum Algorithms. Dr. John Donohue, Scientific Outreach Manager Adaptation of materials by M. Laforest & E. Eleftheriadou. Waves and Particles. Particle. Wave. Wave-particle duality. The Two Golden Rules of Quantum Mechanics. Rule #2

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Wave-Particle Duality and Simple Quantum Algorithms

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  1. Wave-Particle Duality and Simple Quantum Algorithms Dr. John Donohue, Scientific Outreach Manager Adaptation of materials by M. Laforest & E. Eleftheriadou

  2. Waves and Particles Particle Wave

  3. Wave-particle duality

  4. The Two Golden Rules of Quantum Mechanics Rule #2 Measurement uncertainty Rule #1 Superposition A particle can behaveas if it is both “here” and “there” When asked where it is,the particle will be foundeither“here” or “there” Wave behaviour Particle behaviour

  5. Wave-Particle Duality Revisited • Wave and particle picture of a beamsplitter • Interferometry and wave-particle behaviour • Implementing quantum algorithms in the beamsplitter picture • Splitting indivisible particles

  6. Optical Beamsplitters

  7. Waves on a Beamsplitter Glass Coating Phase jump when reflection is from higher to lower index

  8. Photons on a Beamsplitter

  9. Photons on a Beamsplitter

  10. The Mach-Zehnder Interferometer

  11. The Mach-Zehnder Interferometer Constructive Destructive

  12. Constructive Destructive

  13. Constructive Destructive

  14. Photons in an MZI Individual Photon Detections Path Difference Wave-Particle Unity

  15. Quantum Algorithms Algorithms run on quantum machines can have incredible speedups over classical computers But there’s no “recipe” for what problems aquantum computer can help with * P. Kaye, R. Laflamme, M. Mosca. An Introduction to Quantum Computing (2007).

  16. The Deutsch-Josza Algorithm Give a binary function f(x), -> two possible inputs (0 or 1) -> two possible outputs (0 or 1) Determine whether f(x) is constant! Four possible functions:

  17. The Deutsch-Josza Algorithm How many tests do I need to run to know if f(x) is constant? Classically: How many values of f(x) do I need to know?

  18. The Deutsch-Josza Algorithm

  19. The Deutsch-Josza Algorithm f1 f3 • f2 f4

  20. Wave-Particle Duality Revisited Why does the Deutsch-Josza algorithm work? We send in one particle, but because of its wave nature, we effectively probe multiple paths*. *Requires both superposition state as input AND measurement in the superposition basis

  21. Final Thought: Actually Splitting Photons A. Aspect et al. PRL 47, 460–463 (1981)

  22. Final Thought: Actually Splitting Photons Pumplaser pulse Nonlinearcrystal

  23. The No-Cloning Theorem “Cloner”

  24. Thanks! For materials, contact iqc-outreach@uwaterloo.ca @QuantumIQC @quantum_iqc QuantumIQC QuantumIQC 2019 applicationsopen now Three-day PD workshop for Grade 11/12 science teachers. Accommodations, travel, and meals included.

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