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Inaccuracy in Quantum State Tomography - What is to Be Done?

Inaccuracy in Quantum State Tomography - What is to Be Done?

A talk I gave at the 2015 APS Four Corners meeting in Tempe, AZ.

Screencast available at https://youtu.be/D1BVh1sHmXU

Travis Scholten

October 16, 2015
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  1. Inaccuracy in Quantum State Tomography - What is to Be

    Done? Travis L Scholten @Travis_Sch CQuIC @ UNM CCR @ SNL APS Four Corners Meeting ASU @ Tempe, AZ 2015 October 16 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
  2. Let’s talk about characterizing quantum devices. Characterization = Control =

    Computation superconducting circuit ion trap quantum dot
  3. Light is big, in terms of Hilbert space. A bit

    too big. ⇢ = 0 B @ ⇢00 ⇢01 · · · ⇢10 ⇢11 · · · . . . . . . ... 1 C A Estimating quantum state of light requires infinite number of parameters! Density Matrix Wigner function
  4. …and infinity is a big number! ⇢ = 0 B

    @ ⇢00 ⇢01 · · · ⇢10 ⇢11 · · · . . . . . . ... 1 C A Few parameters A lot of parameters! Pretty well understood Not well understood
  5. Is there a finite dimensional estimate which is a good

    model? Depends on what you mean by “good”.
  6. Which is “best” depends on how you score the model.

    Several tools… …such as information criteria… …like the Akaike Information Criterion
  7. The only math formula we need: Goodness of fit Complexity

    Each useless parameter can contribute 1 unit of goodness of fit AIC (model) = 2 log Pr (Data seen | model) + 2(# of parameters)
  8. What about boundaries? What about constraints? Each useless parameter can

    contribute 1 unit of goodness of fit The relationship between uselessness and goodness is subtle.
  9. We need new model selection tools for tomography. Notion of

    effective number of parameters… …which may depend on the true parameter! 0 1 1 2
  10. Images: Wigner function: By Gerd Breitenbach (dissertation) [GFDL (http://www.gnu.org/copyleft/fdl.html) or

    CC-BY- SA-3.0 (http://creativecommons.org/licenses/by-sa/ 3.0/)], via Wikimedia Commons Laser: ”Military laser experiment" by US Air Force - This Image was released by the United States Air Force with the ID 090809-F-5527s-0001 gmon transmon qubit - Michael Fang, John Martinis group, Google; http://web.physics.ucsb.edu/ ~martinisgroup/photos.shtml