Difference between revisions of "Journal Club Autumn 2011"
From Quantum Computing Theory Group
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− | + | 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