Difference between revisions of "Journal Club Autumn 2011"

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Journal Club Spring 2011
+
This quarter we will be focusing on Self-Correcting Quantum Memories
 
 
This quarter we will be focusing on Quantum Error Correction.
 
 
 
Past journal club pages: [[Journal Club Autumn 2010|Autumn 2010]], [[Journal Club Winter 2011|Winter 2011]]
 
  
 
==People==
 
==People==
Line 15: Line 11:
 
==Place==
 
==Place==
  
Friday 2:00pm in Computer Science, CSE 503.
+
Friday 1:30pm in Computer Science, CSE 503.
 +
==Schedule==
 +
{|border="1"
 +
!Subject
 +
!Speaker
 +
!Date
 +
|-
 +
|Introduction and Review 
 +
|  Kamil
 +
|Oct 21
 +
|-
 +
| No-go Theorem for Two Dimensions,  [http://arxiv.org/abs/0810.1983 arXiv:0810.1983] , [[:Media:No2DSelfCorrectingQMemory.pdf | Slides]]
 +
|Isaac
 +
|Oct 28
 +
|-
 +
|3D codes without string operators, Part 1,    [http://arxiv.org/abs/1101.1962 arXiv:1101.1962]
 +
|Lukas and Paul
 +
|Nov 18
 +
|-
 +
|3D codes without string operators, Part 2,    [http://arxiv.org/abs/1101.1962 arXiv:1101.1962]
 +
|Lukas and Paul
 +
|Dec 2
 +
|-
 +
|Energy landscape of 3D Codes, [http://arxiv.org/abs/1105.4159 arXiv:1105.4159] , [[:Media:3DcodesEnergyLandscapePDF.pdf | Slides]]
 +
|Isaac
 +
|Dec 9
 +
|}
 +
 
 +
==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.  
  
==Organization==
 
  
;Possible Topics:
+
----
* Quantum Information
+
===Analysis with Entanglement entropy===
* Self-Correcting Quantum Memories
+
Sep 2011: Stability of topologically invariant order parameters at finite temperature- Kim
* Quantum Category Theory (Dancing Triangles)
+
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.
  
;Topic Chosen
 
: Quantum Error Correction
 
  
;Main ideas:
+
----
 +
===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.
  
==Schedule==
+
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.
  
 +
==Organization==
  
==Papers==
+
;Possible Topics:
 +
* Quantum Information (Mark Wilde http://arxiv.org/abs/1106.1445) (2 votes)
 +
  * 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

Latest revision as of 20:35, 9 December 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, 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

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.

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