# Journal Club Autumn 2011

From Quantum Computing Theory Group

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