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 spin-orbit interaction and large Land\'{e} g-factor 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 zero-mode detection and demonstrate the non-Abelian nature of MZMs by braiding. [2,3,4] To achieve this goal advanced material platforms are needed: low-disorder, single-crystalline, planar networks of nanowires with high spin-orbit energy. In this talk I will discuss the formation and electronic properties of InSb nanowire networks. [5,6] The bottom-up synthesis method we have developed is generic and can be employed to synthesize interconnected nanowire architectures of group III-V, II-VI 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), 1003--1007\newline [2] Alicea, J.; Oreg, Y.; Refael, G.; von Oppen, F.; Fisher, M. P. A. Nat. Phys. 2011, 7 (5), 412--417.\newline [3] Hyart, T. et al. Flux-controlled 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), 859--864\newline [6] Car, D.; Wang, J.; Verheijen, M. A.; Bakkers, E. P. A. M.; Plissard, S. R. Adv. Mater. 2014, 26 (28), 4875--4879. [Preview Abstract] |
Friday, March 17, 2017 8:36AM - 8:48AM |
X46.00002: Berry phase effect on Majorana braiding Yingping He, Baozong Wang, Xiong-Jun Liu Majorana zero modes are predicted to exhibit Non-Abelian braiding, which can be applied to fault-tolerant quantum computation. An essential signature of the non-Abelian braiding is that after a full braiding each of the two Majorana modes under braiding gets a minus sign, namely, a $\pi$ Berry phase. In this work we find a novel effect in Majorana braiding that during the adiabatic transport a Majorana mode may or may not acquire a staggered minus sign under each step that the Majorana is transported, corresponding to two different types of parameter manipulation. This additional minus sign is shown to be a consequence of translational Berry phase effect, which can qualitatively affect the braiding of Majorana modes. Furthermore, we also study the effect of vortices on the Majorana braiding, with the similar additional Berry phase effect being obtained. Our work may provide new understanding of the non-Abelian statistics of Majorana modes and help improve the experiment setup for quantum computation. [Preview Abstract] |
Friday, March 17, 2017 8:48AM - 9:00AM |
X46.00003: Abstract Withdrawn
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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 cold-atom 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 Rydberg-blockade 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 many-body Ramsey interference to extract topological degeneracy and braiding statistics. In the case of a single-layer $\nu=1/m$ 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 m-fold ground-state degeneracy. In the case of bi-layer FQH state connected by tunnels or twist defects, one can create effective genus and hence thread flux into different non-contractible cycles of a torus. One is hence able to do braiding and extract the braiding statistics in the ground-state 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 sub-leading 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 two-dimensional 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 Kramers-Wannier 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 non-topological 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 super-symmetric models. [Preview Abstract] |
Friday, March 17, 2017 9:36AM - 9:48AM |
X46.00007: A constructed toy model by unitary transformation of one-dimensional Ising model and the possibility of topologically ordered ground state Pejman Jouzdani It is known that the ground state of the one-dimensional Ising model cannot be realized in a $\mathbb{Z}_2$ broken-symmetry phase due to a local (single-spin) order parameter. We propose a toy model, constructed from the one-dimensional Ising Hamiltonian by a unitary transformation, that in contrast maintains a symmetry-broken phase and its ground state shows promising protection against single-spin 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 Jordan-Wigner 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, fault-tolerant computation. In this work we turn attention to the Lattice Surgery representation, which realizes encoded logic operations without destroying the intrinsic 2D nearest-neighbor 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 braid-based 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 NP-hard. [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 Non-Clifford gate on a logical qudit encoded in a pair of Z$_{\mathrm{N}}$ parafermionic zero modes via the Aharonov Casher effect. $\surd $Z is a non-Clifford gate for qudits with N greater than 2, where Z is one of the clock operators for an N-level qudit. This gate can be implemented by moving a half fluxon around the pair of parafermionic zero modes that can be realized in a two-dimensional set-up via existing proposals (such as Nature Comm. 4, 1348). The half fluxon can be created as a part of fluxon-antifluxon pair in a Josephson junction made of spinful chiral p-wave superconductors and then moved around the parafermionic zero modes. Supplementing this gate with the measurement based braiding of parafermions with fixed number of topological charge measurements (arXiv$:$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 Fixed-Point Tensor Network States Characterizes Pattern of Long-Range Entanglement Zhu-Xi Luo, Ethan Lake, Yong-Shi Wu The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point 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 fixed-point states leads to an emergence of pre-geometry 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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