Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session X46: Topological Quantum InformationFocus

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Sponsoring Units: GQI Chair: Norman Yao, University of California, Berkeley Room: 393 
Friday, March 17, 2017 8:00AM  8:36AM 
X46.00001: Synthesis of InSb Nanowire Architectures  Building Blocks for Majorana Devices Invited Speaker: Diana Car Breakthroughs in material development are playing a major role in the emerging field of topological quantum computation with Majorana Zero Modes (MZMs). Due to the strong spinorbit interaction and large Land\'{e} gfactor InSb nanowires are one of the most promising one dimensional material systems in which to detect MZMs. [1] The next generation of Majorana experiments should move beyond zeromode detection and demonstrate the nonAbelian nature of MZMs by braiding. [2,3,4] To achieve this goal advanced material platforms are needed: lowdisorder, singlecrystalline, planar networks of nanowires with high spinorbit energy. In this talk I will discuss the formation and electronic properties of InSb nanowire networks. [5,6] The bottomup synthesis method we have developed is generic and can be employed to synthesize interconnected nanowire architectures of group IIIV, IIVI and IV materials as long as they grow along a \textless 111\textgreater direction.\\ \\$[1]$ Mourik, V.; Zuo, K.; Frolov, S. M.; Plissard, S. R.; Bakkers, E. P. A. M.; Kouwenhoven, L. P. Science (80. ). 2012, 336 (6084), 10031007\newline [2] Alicea, J.; Oreg, Y.; Refael, G.; von Oppen, F.; Fisher, M. P. A. Nat. Phys. 2011, 7 (5), 412417.\newline [3] Hyart, T. et al. Fluxcontrolled quantum computation with Majorana fermions. Phys. Rev. B 88, 035121 (2013).\newline [4] Aasen, D.; Hell, M.; Mishmash, R. V.; Higginbotham, A.; Danon, J.; Leijnse, M.; Jespersen, T. S.; Folk, J. A.; Marcus, C. M.; Flensberg, K.; Alicea, J. Phys. Rev. X 6, 031016 (2016).\newline [5] Plissard, S. R.; van Weperen, I.; Car, D.; Verheijen, M. A.; Immink, G. W. G.; Kammhuber, J.; Cornelissen, L. J.; Szombati, D. B.; Geresdi, A.; Frolov, S. M.; Kouwenhoven, L. P.; Bakkers, E. P. A. M. Nat. Nanotechnol. 2013, 8 (11), 859864\newline [6] Car, D.; Wang, J.; Verheijen, M. A.; Bakkers, E. P. A. M.; Plissard, S. R. Adv. Mater. 2014, 26 (28), 48754879. [Preview Abstract] 
Friday, March 17, 2017 8:36AM  8:48AM 
X46.00002: Berry phase effect on Majorana braiding Yingping He, Baozong Wang, XiongJun Liu 
Friday, March 17, 2017 8:48AM  9:00AM 
X46.00003: Abstract Withdrawn It has been recently demonstrated$^1$ that Majorana zero modes may occur in the gapless edge of Abelian quantum Hall states at a boundary between different edge phases bordering the same bulk. Such a zero mode is guaranteed to occur when an edge phase that supports fermionic excitations borders one that does not. Here we generalize to the noncharge conserving case such as may occur when a superconductor abuts the quantum Hall edge. We find that not only Majorana zero modes, but their $\mathbb{Z}_N$ generalizations (known as parafermionic zero modes) may occur at boundaries between edge phases in a fractional quantum Hall state. In particular, we find thst the $\nu=1/3$ fractional quantum Hall state supports topologically distinct edge phases separated by $\mathbb{Z}_3$ parafermionic zero modes when charge conservation is broken. Paradoxically, an arrangement of phases can be made such that only an odd number of localized parafermionic zero modes occur around the edge of a quantum Hall droplet. Such an arrangement is not allowed in a gapped system, but here the paradox is resolved due to an extended zero mode in the edge spectrum. [1] Jennifer Cano, Meng Cheng, Maissam Barkeshli, David J. Clarke, Chetan Nayak, Phys. Rev. B 92, 195152 (2015) 
Friday, March 17, 2017 9:00AM  9:12AM 
X46.00004: Topological interferometer and encoder Guanyu Zhu, Abolhassan Vaezi, Juven Wang, Mohammad Hafezi We propose a topological Ramsey interferometer based on controlled flux insertion in the context of coldatom realization. The synthetic flux inserted into the defects of the topological system is induced by lattice shaking and controlled by an ancilla atom through the Rydbergblockade mechanism. By inserting the flux, one can twist one ground state of the topological system into another, conditioned by the ancilla. One can hence use manybody Ramsey interference to extract topological degeneracy and braiding statistics. In the case of a singlelayer $\nu=1/m$ fractional quantum Hall (FQH) state, the interference pattern acquired from readout of the ancilla qubit has a periodicity of $m\Phi_0$ flux ($2\pi m$ phase) and hence shows an mfold groundstate degeneracy. In the case of bilayer FQH state connected by tunnels or twist defects, one can create effective genus and hence thread flux into different noncontractible cycles of a torus. One is hence able to do braiding and extract the braiding statistics in the groundstate manifold without creating actual anyons. In addition, we show how the ancilla can be used to encode quantum information into the topological qubit, which opens up the possibility of using synthetic topological material as a protected quantum memory. [Preview Abstract] 
Friday, March 17, 2017 9:12AM  9:24AM 
X46.00005: Finite Size Scaling of Topological Entanglement Entropy Yuting Wang, Tobias Gulden, Alex Kamenev We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a subleading term, which scales as $L^{1/\alpha}$ with the size of the subsystem $L$, here $\alpha$ is the R\'{e}nyi index. This term reveals the universal scaling function $h_\alpha(L/\xi)$, where $\xi$ is the correlation length, which is sensitive to the topological index. [Preview Abstract] 
Friday, March 17, 2017 9:24AM  9:36AM 
X46.00006: Duality defects in twodimensional statistical mechanics on the lattice David Aasen, Roger Mong, Paul Fendley We explore applications of topological defect lines in 2D statistical mechanics models on and off the critical point. In particular, we discuss an extension of KramersWannier duality. The duality is implemented by a topological defect line that separates the model from its dual. Away from criticality, we explain how duality defects make it possible to find nontopological defects that localize a topological degree of freedom. In certain cases, this degree of freedom appears in the quantum spin chains as a zero mode. We will elucidate these results with a variety of concrete examples including the Ising, Fibonacci and supersymmetric models. [Preview Abstract] 
Friday, March 17, 2017 9:36AM  9:48AM 
X46.00007: A constructed toy model by unitary transformation of onedimensional Ising model and the possibility of topologically ordered ground state Pejman Jouzdani It is known that the ground state of the onedimensional Ising model cannot be realized in a $\mathbb{Z}_2$ brokensymmetry phase due to a local (singlespin) order parameter. We propose a toy model, constructed from the onedimensional Ising Hamiltonian by a unitary transformation, that in contrast maintains a symmetrybroken phase and its ground state shows promising protection against singlespin perturbation, at least. Using perturbation theory, we argue that the protection is proportional to the system length. However, the unitary transformation used to obtain the model requires a mechanism of coupling of two spins to a tuning external field. We provide numerical evidence that supports the theoretical findings. Due to the relation between the Ising model on an open chain and the Majorana fermion model through the JordanWigner transformation, our model suggests possibility of an alternative approach to experiment topological properties. [Preview Abstract] 
Friday, March 17, 2017 9:48AM  10:00AM 
X46.00008: Optimization of topological quantum algorithms using Lattice Surgery is hard Daniel Herr, Franco Nori, Simon Devitt The traditional method for computation in the surface code or the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits which are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, faulttolerant computation. In this work we turn attention to the Lattice Surgery representation, which realizes encoded logic operations without destroying the intrinsic 2D nearestneighbor interactions sufficient for braided based logic and achieves universality without using defects for encoding information. In both braided and lattice surgery logic there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braidbased logic is proving to be difficult to define and the classical complexity associated with this problem has yet to be determined. In the context of lattice surgery based logic, we can introduce an optimality condition, which corresponds to a circuit with lowest amount of physical qubit requirements, and prove that the complexity of optimizing the geometric (lattice surgery) representation of a quantum circuit is NPhard. [Preview Abstract] 
Friday, March 17, 2017 10:00AM  10:12AM 
X46.00009: Universal Quantum Computing with Parafermions assisted by a half fluxon Arpit Dua, Meng Cheng, Liang Jiang We propose a scheme to perform a NonClifford gate on a logical qudit encoded in a pair of Z$_{\mathrm{N}}$ parafermionic zero modes via the Aharonov Casher effect. $\surd $Z is a nonClifford gate for qudits with N greater than 2, where Z is one of the clock operators for an Nlevel qudit. This gate can be implemented by moving a half fluxon around the pair of parafermionic zero modes that can be realized in a twodimensional setup via existing proposals (such as Nature Comm. 4, 1348). The half fluxon can be created as a part of fluxonantifluxon pair in a Josephson junction made of spinful chiral pwave superconductors and then moved around the parafermionic zero modes. Supplementing this gate with the measurement based braiding of parafermions with fixed number of topological charge measurements (arXiv$:$1607.07475) provides the avenue for universal quantum computing with parafermions.~ [Preview Abstract] 
Friday, March 17, 2017 10:12AM  10:24AM 
X46.00010: The Structure of FixedPoint Tensor Network States Characterizes Pattern of LongRange Entanglement ZhuXi Luo, Ethan Lake, YongShi Wu The algebraic structure of representation theory naturally arises from 2D fixedpoint tensor network states, which conceptually formulates the pattern of longrange entanglement realized in such states. In 3D, the same underlying structure is also shared by TuraevViro statesum topological quantum field theory (TQFT). We show that a 2D fixedpoint tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixedpoint states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global onsite unitary symmetry is imposed on the tensor network states. [Preview Abstract] 
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