1 / 32

Quantum Computing with Noninteracting Particles

Quantum Computing with Noninteracting Particles. Alex Arkhipov. Noninteracting Particle Model. Weak model of QC Probably not universal Restricted kind of entanglement Not qubit-based Why do we care? Gains with less quantum Easier to build Mathematically pretty. Classical Analogue.

gwidon
Download Presentation

Quantum Computing with Noninteracting Particles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quantum Computing with Noninteracting Particles Alex Arkhipov

  2. Noninteracting Particle Model • Weak model of QC • Probably not universal • Restricted kind of entanglement • Not qubit-based • Why do we care? • Gains with less quantum • Easier to build • Mathematically pretty

  3. Classical Analogue

  4. Balls and Slots

  5. Transition Matrix

  6. A Transition Probability ?

  7. A Transition Probability

  8. A Transition Probability

  9. A Transition Probability

  10. A Transition Probability

  11. A Transition Probability

  12. A Transition Probability

  13. Probabilities for Classical Analogue

  14. Probabilities for Classical Analogue • What about other transitions? ? ?

  15. Configuration Transitions Transition matrix for one ball Transition matrix for two-ball configurations m=3, n=1 m=3, n=2

  16. Classical Model Summary • n identical balls • m slots • Choose start configuration • Choose stochastic transition matrix M • Move each ball as per M • Look at resulting configuration

  17. Quantum Model

  18. Quantum Particles • Two types of particle: Bosons and Fermions Bosons Fermions (Slide concept by Scott Aaronson)

  19. Identical Bosons ?

  20. Identical Fermions ?

  21. Algebraic Formalism • Modes are single-particle basis states • Variables • Configurations are multi-particle basis states • Monomials • Identical bosons commute • Identical fermions anticommute

  22. Example: Hadamarding Bosons Hong-Ou-Mandel dip

  23. Example: Hadamarding Fermions

  24. Definition of Model m×m unitary U x2 U x2 U x1 n particles U x4 U x5 Initial configuration

  25. Complexity

  26. Complexity Comparison Adaptive → BQP [KLM ‘01]

  27. Bosons are Hard: Proof • Classically simulate identical bosons • Using NP oracle, estimate AAAAAAA XXXXXXXXXXX • Compute permanent in BPPNP • P#P lies within BPPNP • Polynomial hierarchy collapses Approx counting Reductions Perm is #P-complete Toda’s Theorem

  28. ApproximateBosons are Hard: Proof • Classically approximately simulate identical bosons • Using NP oracle, estimate of random M with high probability • Compute permanent in BPPNP • P#P lies within BPPNP • Polynomial hierarchy collapses Approx counting Random self-reducibility + conjectures Perm is #P-complete Toda’s Theorem

  29. Experimental Prospects

  30. Linear Optics • Photons and half-silvered mirrors • Beamsplitters + phaseshifters are universal

  31. Challenge: Do These Reliably • Encode values into mirrors • Generate single photons • Have photons hit mirrors at same time • Detect output photons

  32. Proposed Experiment • Use m=20, n=10 • Choose U at random • Check by brute force!

More Related