1 / 31

Title slide

Title slide. PQE 2003. Quantum information with photons and atoms: from tomography to error correction. C. W. Ellenor, M. Mohseni, S.H. Myrskog, J.K. Fox, J. S. Lundeen, K. J. Resch, M. W. Mitchell, and Aephraim M. Steinberg

xylia
Download Presentation

Title slide

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. Title slide PQE 2003 Quantum information with photons and atoms: from tomography to error correction C. W. Ellenor, M. Mohseni, S.H. Myrskog, J.K. Fox, J. S. Lundeen, K. J. Resch, M. W. Mitchell, and Aephraim M. Steinberg Dept. of Physics, University of Toronto

  2. Acknowledgments U of T quantum optics & laser cooling group: PDF: Morgan Mitchell Optics: Kevin Resch ( Wien) Jeff Lundeen Chris Ellenor ( Korea) Masoud Mohseni Reza Mir ( Lidar) Atom Traps: Stefan Myrskog Jalani Fox Ana Jofre Mirco Siercke Salvatore Maone Samansa Maneshi TBA: Rob Adamson Theory friends: Daniel Lidar, Janos Bergou, John Sipe, Paul Brumer, Howard Wiseman

  3. OUTLINE • Introduction: • Photons and atoms are promising for QI. • Need for real-world process characterisation • and tailored error correction. • No time to say more. • Quantum process tomography on entangled photon pairs • - E.g., quality control for Bell-state filters. • - Input data for tailored Quantum Error Correction. • An experimental application of decoherence-free • subspaces in a quantum computation. • Quantum state (and process?) tomography on • center-of-mass states of atoms in optical lattices. • Coming attractions…

  4. Density matrices and superoperators

  5. Two-photon Process Tomography "Black Box" 50/50 Beamsplitter Two waveplates per photon for state preparation Detector A HWP HWP PBS QWP QWP SPDC source QWP QWP PBS HWP HWP Detector B Argon Ion Laser Two waveplates per photon for state analysis

  6. Hong-Ou-Mandel Interference > 85% visibility for HH and VV polarizations HOM acts as a filter for the Bell state:  = (HV-VH)/√2 Goal: Use Quantum Process Tomography to find the superoperator which takes in  out Characterize the action (and imperfections) of the Bell- State filter.

  7. “Measuring” the superoperator Coincidencences Output DM Input } HH } } 16 input states } HV etc. VV 16 analyzer settings VH

  8. “Measuring” the superoperator Superoperator Input Output DM HH HV VV VH Output Input etc.

  9. “Measuring” the superoperator Superoperator Input Output DM HH HV VV VH Output Input etc.

  10. Testing the superoperator LL= input state Predicted Nphotons = 297 ± 14

  11. Testing the superoperator LL= input state Predicted Nphotons = 297 ± 14 Observed Nphotons = 314

  12. So, How's Our Singlet State Filter? Bell singlet state:  = (HV-VH)/√2 Observed  

  13. Model of real-world beamsplitter Singlet filter multi-layer dielectric AR coating 45° “unpolarized” 50/50 dielectric beamsplitter at 702 nm (CVI Laser) birefringent element + singlet-state filter + birefringent element

  14. Model beamsplitter predicitons Singlet filter Best Fit: 1 = 0.76 π 2 = 0.80 π Predicted

  15. Comparison to measured Superop Observed Predicted Predicted

  16. Performing a quantum computation in a decoherence-free subspace y f(x) The Deutsch-Jozsa algorithm: A Oracle A H x x H y H We use a four-rail representation of our two physical qubits and encode the logical states 00, 01, 10 and 11 by a photon traveling down one of four optical rails numbered 1, 2, 3 and 4, respectively. Photon number basis Computational basis 1 1st qubit 2nd qubit 2 3 4

  17. Error model and decoherence-free subspaces 11 11 10 eif 10 00 00 01 eif 01 But after oracle, only qubit 1 is needed for calculation. Encode this logical qubit in either DFS: (00,11) or (01,10). Consider a source of dephasing which acts symmetrically on states 01 and 10 (rails 2 and 3)… Modified Deutsch-Jozsa Quantum Circuit H x x H y y f(x) H

  18. DJ experimental setup Experimental Setup Random Noise 1 2 1 3 4 23 2 Preparation 3 4 Oracle 3/4 B Optional swap for choice of encoding D Phase Shifter 4/3 C A PBS Detector Waveplate Mirror

  19. DJ without noise -- raw data Constant function Balanced function C B Original encoding DFS Encoding C B C B B C B C

  20. DJ with noise-- results Original Encoding DFS Encoding C B C B B C B C Constant function Balanced function C B

  21. Tomography in Optical Lattices Part I: measuring state populations in a lattice…

  22. Houston, we have separation!

  23. Quantum state reconstruction p p =x t x x Initial phase- space distribution Wait… Shift… p Q(0,0) = Pg x Measure ground state population (More recently: direct density-matrix reconstruction)

  24. Quasi-Q (Pg versus shift) for a 2-state lattice with 80% in upper state.

  25. Exp't:"W" or [Pg-Pe](x,p)

  26. W(x,p) for 80% excitation

  27. Coming attractions • A "two-photon switch": using quantum enhancement of • two-photon nonlinearities for • - Hardy's Paradox (and weak measurements) • - Bell-state determination and quantum dense coding(?) • Optimal state discrimination/filtering (w/ Bergou, Hillery) • The quantum 3-box problem (and weak measurements) • Process tomography in the optical lattice • - applying tomography to tailored Q. error correction • Welcher-Weg experiments (and weak measurements, w/ Wiseman) • Coherent control in optical lattices (w/ Brumer) • Exchange-effect enhancement of 2x1-photon absorption • (w/ Sipe, after Franson) • Tunneling-induced coherence in optical lattices • Transient anomalous momentum distributions (w/ Muga) • Probing tunneling atoms (and weak measurements) • … et cetera

  28. Schematic of DJ Schematic diagram of D-J interferometer Interfering 1 with 4 and 2 with 3 is as effective as interfering 1 with 3 and 2 with 4 -- but insensitive to this decoherence model. 1 2 3 4 Oracle 1 00 2 01 3 10 4 11 1 2 4 3 “Click” at either det. 1 or det. 2 (i.e., qubit 1 low) indicates a constant function; each looks at an interferometer comparing the two halves of the oracle.

  29. Quantum state reconstruction Wait… Shift… Initial phase- space distribution Measure ground state population

  30. Q(x,p) for a coherent H.O. state

  31. Theory for 80/20 mix of e and g

More Related