Journal Club Autumn 2011

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


Organizer(1): Paul Pham (

Organizer(2): Lukas Svec (

Faculty Advisor: Aram Harrow (


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


Subject Speaker Date
Introduction and Review Kamil Oct 21
No-go Theorem for Two Dimensions, arXiv:0810.1983 , Slides Isaac Oct 28
3D codes without string operators, Part 1, arXiv:1101.1962 Lukas and Paul Nov 18
3D codes without string operators, Part 2, arXiv:1101.1962 Lukas and Paul Dec 2
Energy landscape of 3D Codes, arXiv:1105.4159 , Slides Isaac Dec 9


Ideas before 2009

Jul 2009: Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem 
               codes- Chesi, Loss, Bravyi, Terhal
   - 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
    -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
   - 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
   - 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
   - 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
   - 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
   - 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
   - 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 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
   - 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
   - Extension of Bravyi's paper (July 2009) that proves the stability of gaps using Anderson localization.


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
 * 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 (
  * Con: hard! (e.g. quantum PCP)
  • Quantum Money / Knots
  • Stephen Bartlett