Symposium on Topological Quantum Computation

4 Jun 2011, 09:00 → 5 Jun 2011, 17:00 Europe/Stockholm

132:028 (Nordita)

Ville Lahtinen (Nordita)

The next Symposium on Topological Quantum Computation will be held at NORDITA, Stockholm, on June 4-5th, 2011.

The idea is to have a small relaxed two day workshop, that in the spirit of the previous events allows plenty of time for informal discussions between the talks. The focus of the symposium will be the interplay of topological order and quantum information theory. The topics will range from implementations of topological quantum computation to employing quantum information techniques in understanding topologically ordered condensed matter systems.

The list of speakers:

• B. Andrei Bernevig (Princeton University)
• Felix von Oppen (Freie Universität Berlin)
• James Wootton (University of Leeds)
• Cyril Stark (ETH Zürich)
• Janik Kailasvuori (MPI Dresden)
• Shanna Haaker (University of Amsterdam)
• Michael Kamfor / Marc Daniel Schulz (University of Dortmund)
• Enrique Rico Ortega (University of Innsbruck)
• Ivan Rodriguez (NUI Maynooth)
• Sofyan Iblisdir (University of Barcelona)

Internet access

Nordita does not have an own wireless network. Internet access is provided through the campus network, which, however, requires pre-registration from guests. Should you want to use it, please provide us with your date of birth before Wednesday 1st of June. Alternatively you may also use the eduroam network if you have access to it through your home institution.

Poster session

There were quite a few more contributions than we had slots for talks. Thus we are organizing a poster session on Saturday where further works can be presented. If you are interested in bringing a poster, please let us know so that we can arrange for sufficient amount of stands.

Registration
There are no registration fees. To register, simply e-mail Ville Lahtinen (villel@kth.se) that you would like to participate.

Accommodation:

The block booking has expired. You are still welcome to participate the symposium, but you will be responsible for your own accommodation. We would recommend still acting soon as finding suitable accommodation can be problematic in Stockholm. Some conveniently located hotels can be found here.

Saturday 4 June

1 Bringing order through disorder: Localization in the toric code (James Wootton, University of Leeds)

Anderson localization emerges in quantum systems when randomised parameters cause the exponential suppression of motion. In this talk we will consider the localization phenomenon in the toric code, demonstrating its ability to sustain quantum information in a fault tolerant way. We show that an external magnetic field induces quantum walks of anyons, causing logical information to be destroyed in a time linear with the system size when even a single pair of anyons is present. However, by taking into account the disorder inherent in any physical realisation of the code, it is found that localization allows the memory to be stable in the presence of a finite anyon density. Enhancements to this effect are also considered using random lattices.

2 Localization of Toric Code defects (Cyril Stark, ETH Zürich)

We explore the possibility of passive error correction in the toric code model. We first show that even coherent dynamics, stemming from spin interactions or the coupling to an external magnetic field,  lead to logical errors. We then argue that Anderson localization of the defects, arising from unavoidable fluctuations of the coupling constants, provides a remedy. This protection is demonstrated using general analytical arguments that are complemented with numerical results which demonstrate that self-correcting memory can in principle be achieved in the limit of a nonzero density of identical defects. The talk is mainly based on arXiv:1101.6028.

11:00 Coffee

3 Critical breakdown of perturbed topological phases (Michael Kamfor and Marc Daniel Schulz, University of Dortmund)

We explore critical quantum phase transitions of the celebrated Z2-toric-code model and its Z3 generalization in the presence of a magnetic field. The zero-temperature phase diagram is determined by combining strong-coupling expansions (pCUTs) and variational methods (iPEPS). Interestingly, we find a multi-critical line with exotic properties for the Z2 case. For the generalized Z3-toric-code we find critical lines in parameter space which fall in the 3d xy universality class. The latter can be rigorously shown for special cases using exact mappings to the antiferromagnetic Potts model.

12:15 Lunch

4 Topological phases and Majorana end states in disordered quantum wires (Felix von Oppen, Freie Universität Berlin)

Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing [1,2]. In this talk, I discuss how potential disorder affects the topological phase by a combination of analytical and numerical approaches. We find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire [3]. We also obtain the entire distribution function of the energy of the Majorana end states as well as of the lowest bulk state in wires of finite length, and discuss the implications for the speed at which a hypothetical topological quantum computer can be operated [4]. [1] Y. Oreg, G. Refael, F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett. 105, 177002 (2010) [2] J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.P.A. Fisher, Non-Abelian statistics and topological quantum computation in 1D wire networks, Nature Physics 7, 412 (2011) [3] P. W. Brouwer, M. Duckheim, A. Romito, F. von Oppen, Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling, arXiv:1103.2746 [4] P. W. Brouwer, M. Duckheim, A. Romito, F. von Oppen, Probability distribution of Majorana end state energies in disordered wires, arXiv:1104.1531.

5 Kaleidoscope of topological phases with multiple Majorana species (Janik Kailasvuori, MPI Dresden)

Exactly solvable lattice models for spins or hopping fermions provide fascinating examples of topological phases. Some of them support localized Majorana fermions, which feature in topologically protected quantum computing. The Chern invariant $\nu$ is one important characterization of such phases. Systems with arbitrarily large Chern numbers are known, but systems supporting Majorana fermions have mainly provided ground states with $\nu=0,\pm1$ although symmetry arguments in some cases allow for any integer $\nu$. With the rich variety of phases exhibited by spin-triplet p-wave fermions in mind, we look at the square-octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and indeed enjoys a rich phase diagram featuring distinct abelian and nonabelian phases with $\nu= 0,\pm1,\pm2,\pm3$ and $ \pm4$. The $\nu=\pm1 $ and $\nu=\pm3$ phases all support localized Majorana modes and are examples of Ising and $SU(2)_2$ anyon theories respectively. We show that transitions between topological phases are accompanied by stepwise transfer of Chern number between the four bands and then finally describe the edge spectra at topological domain walls, highlighting the one between distinct $\nu=0$ phases.

15:45 Coffee

6 Topology by Dissipation in Atomic Quantum Wires (Enrique Rico Ortega, University of Innsbruck)

Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been exclusively discussed in a Hamiltonian context, we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems with engineered dissipation. The specific system studied here is a quantum wire of spinless atomic fermions in an optical lattice coupled to a bath. The key feature of the dissipative dynamics described by a Lindblad master equation is the existence of Majorana edge modes, representing a non-local decoherence free subspace. The isolation of the edge states is enforced by a dissipative gap in the p-wave paired bulk of the wire. We describe dissipative non-Abelian braiding operations within the Majorana subspace, and we illustrate the insensitivity to imperfections. Topological protection is granted by a nontrivial winding number of the system density matrix. -Authors: S. Diehl, E. Rico, M.A. Baranov, P. Zoller -Reference: arXiv:1105.5947

16:45 Poster session and refreshments

Sunday 5 June

7 Tutorial on entanglement spectrum (Andrei Bernevig, Princeton University)

TBA

11:00 Coffee

8 Boundary quantum critical phenomena with entanglement renormalization (Sofyan Iblisdir, University of Barcelona)

TBA

12:15 Lunch

9 Particles in non-Abelian gauge potentials: Landau problem and insertion of non-Abelian flux (Shanna Haaker, University of Amsterdam)

This talk will be on charged spin-1/2 particles in two dimensions, subject to a non-Abelian magnetic field. A quick review will be given on artificial gauge potentials in the cold atomic setting, which is an ideal simulator of our desired system of charged particles. Next, the single-particle spectrum on the plane and sphere geometry is presented in the presence of a uniform non-Abelian gauge potential. The final part of this talk will deal with the adiabatic insertion of non-Abelian flux in a spin-polarized integer quantum Hall state, leading to the formation of quantum Hall Skyrmions. The results presented here can be found in our recently published paper: B. Estienne, S.M. Haaker and K. Schoutens, New J. Phys. 13 045012 (2011)

10 Excitations of the Moore-Read fractional quantum Hall state (Ivan Rodriguez, NUI Maynooth)

Moore and Read's Pfaffian wave function remains one of the leading candidates for the description of the electronic ground state of the fractional quantum Hall plateaux at filling $\nu$ = 5/2. Much effort has been devoted to understanding the quasihole excitations but not much is known about the quasielectron excitations and about the neutral excitations (excitons), which can be viewed as combinations of quasiholes and quasielectrons. In this talk, we propose trial wave functions for quasielectron and exciton excitations for the Pfaffian fractional quantum Hall state and study these numerically. The trial wave functions are shown to have good overlaps with wave functions obtained by exact diagonalization of the model 3-body Hamiltonian for which the Pfaffian state is an exact zero energy ground state of maximal density.