Difference between revisions of "Journal Club Autumn 2011"
From Quantum Computing Theory Group
(Created page with "Journal Club Spring 2011 This quarter we will be focusing on Quantum Error Correction. Past journal club pages: Autumn 2010, [[Journal Club Winter ...") |
(→Schedule) |
||
(42 intermediate revisions by 5 users not shown) | |||
Line 1: | Line 1: | ||
− | + | This quarter we will be focusing on Self-Correcting Quantum Memories | |
− | |||
− | This quarter we will be focusing on Quantum | ||
− | |||
− | |||
==People== | ==People== | ||
Line 15: | Line 11: | ||
==Place== | ==Place== | ||
− | Friday | + | 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. | ||
+ | |||
+ | |||
+ | ---- | ||
+ | ===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: | |
+ | * 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
Contents
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
- 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