Difference between revisions of "Journal Club Autumn 2011"

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Revision as of 06:07, 26 October 2011

Journal Club Spring 2011

This quarter we will be focusing on Self-Correcting Quantum Memories

People

Organizer(1): Paul Pham (ppham@cs.washington.edu)

Organizer(2): Lukas Svec (svecl@u.washington.edu)

Faculty Advisor: Aram Harrow (aram@cs.washington.edu)

Place

Friday 1:30pm in Computer Science, CSE 503.

Schedule

Subject Speaker Date
Introduction and Review Kamil Oct 21
No-go Theorem for Two Dimensions Isaac Oct 28
Nov 4
Nov 11
Nov 18
Dec 2
Dec 9

Organization

Possible Topics
  * Pro/Con: field has stabilized, stuck on solving additivity problem
  * Con: unrealistic models, not as applicable
  * Pro: Using asymptotic bounds on entropy can give classical algorithm for approximating separable states. (Brandao, Christandl, Yard)
  * Pro: connection to quantum error-correcting codes
  • Self-Correcting Quantum Memories (5 votes)
 * Pro: hot/active research area right now, possibility of making contribution, not many people working on
   * Major breakthrough by Haah http://arxiv.org/abs/1101.1962
 * Pro: best way theory can help build a quantum computer
 * Pro: nice connections to statistical physics (topological order)
  • Matt Hastings / Sergei Bravyi / Alexei Kitaev (Greatest Hits, Vol. 1) (0 votes)
  * Hastings: area laws, Lieb-Robinson bounds, additivity, classical algorithms for simulating quantum systems, hamiltonian complexity, self-correcting quantum memory, topological order
  * Bravyi: stoquastic hamiltonians, topological codes, Majorana fermions, stability results for topological order
  * Kitaev: awesome
  * Possibly invite for physics colloquium
  • Oded Regev: quantum algorithms, communication complexity, lattice-based crypto (1 vote)
  • Following one particular person:
  * Pro: can jump around various topics, get good breadth
  * Con: might not ever understand anything
  • Hamiltonian Complexity (3 votes)
  * Pro: has great obscure acronyms, in the intersection of physics and CS (Lieb-Robinson, area laws, etc.), good guide / survey by Tobias Osborne (http://arxiv.org/abs/1106.5875)
  * Con: hard! (e.g. quantum PCP)
  • Quantum Money / Knots
  • Stephen Bartlett

Papers

Ideas before 2009:

Jul 2009: Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem 
               codes- Chesi, Loss, Bravyi, Terhal
http://arxiv.org/abs/0907.2807
   - more general discussion of self-correcting memories



No-go theorems

Oct 2010: A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes- Terhal
http://arxiv.org/abs/0810.1983
    -A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
Mar 2011: Feasibility of self-correcting quantum memory and thermal stability of topological order- Yoshida
http://arxiv.org/abs/1103.1885
   - This beast of a no-go theorem by Yoshida

and another Hastings paper 1106.6026


3D codes without strings

Dec 2010: Exactly solvable 3D quantum model with finite temperature topological order- Kim 
http://arxiv.org/abs/1012.0859
   - First of a series of papers on the idea of finding 3D models that have topological stability at 
      finite temperature. Haah extends this by finding codes with simpler unit cells (Jan & May 2011). 
Dec 2010: Logical operator tradeoff for local quantum codes- Haah and Preskill
http://arxiv.org/abs/1011.3529
   - no-go theorem with Preskill showing that 2D communting projector codes are not sufficiently 
      self correcting. This is the starting point to Haah's series of papers.  
Jan 2011: Local stabilizer codes in three dimensions without string logical operators- Haah
http://arxiv.org/abs/1101.1962
   - In 2D, string logical operators do not lead to self-correcting memories as proved by Terhal. Here, Haah finds 18 
      codes in 3D that do not have such string operators. These could be self-correcting.
May 2011: On the energy landscape of 3D spin Hamiltonians with topological order- Haah and Bravyi
http://arxiv.org/abs/1105.4159
   - Extension on Haah's paper that analyzes one of the 18 3D codes from his Jan 2011 paper and finds 
      that it has a O(log n) energy barrier. Uses neat renormalization techniques. 



Analysis with Entanglement entropy

Sep 2011: Stability of topologically invariant order parameters at finite temperature- Kim
http://arxiv.org/abs/1109.3496
   - Looks to see if entanglement entropy is maintained in perturbed systems that have non-zero 
      entanglement entropy. (Topological entanglement entropy was defined in 2005 by Kitaev and 
      Preskill in http://arxiv.org/abs/hep-th/0510092.) Non-zero ent. entropy is found in systems 
      that store quantum information.



Anderson localization techniques

Aug 2011: Disorder-assisted error correction in Majorana chains - Bravyi and Koenig
http://arxiv.org/abs/1108.3845
   - Using disorder to improve topological codes. Maps the chain to a 1D Andersen model in which 
      eigenvectors are localized states.
Sep 2011: Stability of Frustration-Free Hamiltonians- Michalakis, Pytel
http://arxiv.org/abs/1109.1588
   - Extension of Bravyi's paper (July 2009) that proves the stability of gaps using Anderson localization.