Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session Y27: Focus Session: Semiconductor Qubits- In Search of Majorana |
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Sponsoring Units: GQI Chair: Gil Refael, California Institute of Technology Room: C155 |
Friday, March 25, 2011 8:00AM - 8:12AM |
Y27.00001: Non-Abelian statistics and topological quantum information processing in 1D wire networks Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, Matthew P.A. Fisher Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key operations---braiding of non-Abelian anyons---can be implemented in one-dimensional semiconductor wire networks. Previous work [Lutchyn et al., arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly, we show that networks of such wires allow braiding of Majorana fermions and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental setups that enable the Majorana fusion rules to be probed, along with networks that allow for efficient exchange of arbitrary numbers of Majorana fermions. This work paves a new path forward in topological quantum computation that benefits from physical transparency and experimental realism. [Preview Abstract] |
Friday, March 25, 2011 8:12AM - 8:24AM |
Y27.00002: Majorana fermions in nanowires without gating superconductors Chien-Hung Lin, Hoi Yin Hui, Jay Sau, Sankar Das Sarma Majorana fermions have been proposed to be realizable at the end of the semiconductor nanowire on top of an s-wave superconductor [1,2]. These proposals require gating the nanowire directly in contact with a superconductor which may be difficult in experiments. We analyze [1,2] in configurations where the wire is only gated away from the superconductor. We show that some signatures of the Majorana mode remain but the Majorana mode is not localized and hence not suitable for quantum computation. Therefore we propose an 1D periodic heterostructure which can support localized Majorana modes at the end of the wire without gating on the superconductor. \\[4pt] [1] Jay D. Sau et al., arXiv:1006.2829, Phys Rev B (in press)\\[0pt] [2] Roman M. Lutchyn et al., Phys. Rev. Lett. 105, 077001 (2010) [Preview Abstract] |
Friday, March 25, 2011 8:24AM - 8:36AM |
Y27.00003: Effects of Interactions on a Topological Phase Exhibiting Majorana Fermions in Quantum Wires Miles Stoudenmire, Jason Alicea The ability to create and manipulate Majorana fermions in condensed matter systems is not only of fundamental interest for understanding topological phases but also provides a realistic route toward quantum computation. Recently, a series of devices have been proposed that could realize exotic Majorana physics in relatively conventional settings; among the most promising is a superconducting wire system with strong spin-orbit coupling. Because superconducitivity is induced in this system by proximity effect, the system remains superconducting even with net repulsive interactions. The effects of such interactions on this system have until now remained unexplored. Using the Density Matrix Renormalization Group method, we explore the fate of the topological phase in the presence of interactions. Obtaining a matrix product state representation of the degenerate ground states is especially helpful as it allows us to determine detailed properties of the Majorana edge states. Furthermore, we find that interactions significantly expand the topological region of the phase diagram, a result which strengthens proposals to realize Majorana fermions in such wire systems experimentally. [Preview Abstract] |
Friday, March 25, 2011 8:36AM - 8:48AM |
Y27.00004: The exchange statistics of Majorana fermions in quasi-one-dimensional networks David J. Clarke, Jay D. Sau, Sumanta Tewari Under appropriate external conditions a semiconductor with strong spin-orbit coupling in proximity to an $s$-wave superconductor can be in a topological superconducting (TS) phase. In the topological phase, various defects of the order parameter trap zero energy excitations called Majorana bound states. In a wire geometry the relevant defects are the two ends of the topological region, and each traps a localized zero energy excitation. A network of such wires allows the pairwise exchange of the Majorana bound states. Alicea et al. have shown that these bound states obey non- Abelian exchange statistics, and have proposed [1] such a system as a platform for topological quantum computation (TQC). Here we show that the particular realization of non- Abelian statistics produced in a Majorana wire network is highly dependent on the local properties of individual wire junctions. For a simply connected network, the possible realizations can be characterized by the chirality of individual junctions. We demonstrate how this chirality may be calculated for a particular junction. There is in general no requirement for junction chiralities to remain consistent across a wire network. Careful control of the junction chirality is required for TQC applications of Majorana wire networks. [1] J. Alicea et al., arXiv:1006.4395. [Preview Abstract] |
Friday, March 25, 2011 8:48AM - 9:00AM |
Y27.00005: Interferometry and topological quantum computation using Majorana Fermions at semiconductor/superconductor interfaces Jay Sau, Sumanta Tewari, Sankar Das Sarma Majorana Fermions are hitherto unobserved exotic Fermionic excitations, which are their own anti-particles. Recently, a lot of excitement has been generated by proposals to realize Majorana fermions in topological superconductors in a rather general class of topological superconductors, some of which may be as simple as the interface 1D or 2D InAs and Al in the appropriate parameter regime might have exotic topological properties and Majorana Fermions [1]. In my talk, I will discuss recent proposals for performing interferometry in 2D and 1D versions of such systems [2] together with ideas for performing Quantum Computation [3] using such robust Majorana fermion based qubits. \\[4pt] [1] J. Sau, S. Tewari, R. Lutchyn, T. Stanescu, S. Das Sarma, arxiv:1006.2829 PRB (in press). [2] J. Sau, S. Tewari, S. Das Sarma, arxiv:arXiv:1004.4702. [3] J. Sau, S. Tewari, S. Das Sarma, arxiv:arXiv:1007.4204 PRA(in press) [Preview Abstract] |
Friday, March 25, 2011 9:00AM - 9:12AM |
Y27.00006: Topological Phases in Dissipative Quantum Transport Mark Rudner, Michael Levin, Leonid Levitov Recently, a new type of topological quantization was discovered in dissipative quantum transport on a one dimensional bipartite lattice with decay [1]. The transition between distinct topological phases is accompanied by a discontinuous change in the expected displacement covered by a particle before it decays. Here we show that this behavior extends to a much wider family of models, and provide a prescription for computing the topological invariant which distinguishes all of the phases which arise in the general case. When the underlying hopping problem without decay possesses time reversal symmetry, we show that the expected displacement, averaged with respect to all initial states, is quantized. The topological nature of this phenomenon, which is unique to systems with decay, places it on a similar footing as other robust topological phenomena such as the quantization of the Hall conductance [2], or of the adiabatically-pumped charge in periodically-driven 1D systems [3]. Correspondingly, here we find that quantization is robust against a range of perturbations and certain types of decoherence. Similarities and differences with the phases of one-dimensional topological insulators will be discussed. [1] M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009). [2] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982). [3] D. J. Thouless, Phys. Rev. B 27, 6083 (1983). [Preview Abstract] |
Friday, March 25, 2011 9:12AM - 9:24AM |
Y27.00007: Counting Majorana zero modes in superconductors Luiz Santos, Yusuke Nishida, Claudio Chamon, Christopher Mudry We present a counting formula for computing the number of (Majorana) zero modes bound to topological point defects. The counting formula is evaluated in a gradient expansion for systems with charge-conjugation symmetry. We will consider examples that include Dirac fermions and the chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers. [Preview Abstract] |
Friday, March 25, 2011 9:24AM - 9:36AM |
Y27.00008: Non-Abelian order in s-wave superconductors: Phases and quantum transitions Sumanta Tewari, Tudor Stanescu, Jay Sau, Parag Ghosh, Sankar Das Sarma Non-Abelian topological superconductivity has been predicted to occur in s-wave superconductors with a sizable spin-orbit (SO) coupling. As is now well known, such a system can be used for topological quantum computation. When an external Zeeman splitting crosses a critical value, the system passes from a regular, non-topological, superconducting phase to a topological one. On the other hand, in the absence of SO coupling this critical value corresponds to the Zeeman splitting above which the system loses its s-wave superconductivity. We are thus led to the paradoxical conclusion that the topological superconducting phase appears in a parameter regime at which the system actually is non- superconducting in the absence of SO coupling. In this work we resolve this paradox. [Preview Abstract] |
Friday, March 25, 2011 9:36AM - 9:48AM |
Y27.00009: Induced Chiral f-wave Superconducting Pairing and Majorana Fermions in a Hole-doped Semiconductor Chuanwei Zhang, Li Mao, Junren Shi, Qian Niu We show that a chiral f + if-wave superconducting pairing may be induced in the lowest heavy hole band of a hole-doped semiconductor thin film through proximity contact with an s-wave superconductor. The chirality of the pairing originates from the 3$\pi$ Berry phase accumulated for a heavy hole moving along a close path on the Fermi surface. There exist three chiral gapless Majorana edge states, in consistence with the chiral f + if-wave pairing. We show the existence of zero energy Majorana fermions in vortices in the semiconductor-superconductor heterostructure by solving the Bogoliubov-de-Gennes equations numerically as well as analytically in the strong confinement limit. The proposed semiconductor/superconductor heterostructure can be used as a platform for observing non-Abelian statistics and performing TQC. [Preview Abstract] |
Friday, March 25, 2011 9:48AM - 10:00AM |
Y27.00010: Anyonic entanglement renormalization Robert Koenig, Ersen Bilgin We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions. [Preview Abstract] |
Friday, March 25, 2011 10:00AM - 10:12AM |
Y27.00011: Protected phase gates for superconducting qubits Peter Brooks, John Preskill Quantum systems with inherent error-correcting properties offer a powerful tool for building quantum computers to be insensitive to the effects of errors. Kitaev [arXiv:cond-mat/0609441] has proposed an intrinsically fault-tolerant qubit design based on superconducting systems. The phase gate $\Lambda(i)$ in this system is performed by coupling the qubit to a quantum $LC$ oscillator for a period of time. The evolution of the oscillator can be understood as being protected by a family of continuous variable quantum codes at every point in its evolution, providing natural robustness against random variations in the duration and strength of the coupling. We present the results of numerical simulations of this system which investigate the fidelity of the phase gate operation as a function of the duration mistiming. We discuss the robustness of the gate under the effect of anharmonic perturbations to the oscillator and oscillator coupling, and adiabaticity requirements for this scheme to properly function. [Preview Abstract] |
Friday, March 25, 2011 10:12AM - 10:24AM |
Y27.00012: Resilience of Topological Codes to Depolarization Ruben S. Andrist, Hector Bombin, Miguel Angel Martin-Delgado, Helmut G. Katzgraber Standard error correction is based on redundant storage of quantum information. However, in topological quantum error correction decoherence effects are prevented by encoding logical qubits in nonlocal degrees of freedom, while actively correcting for errors that occur locally in the system. Previous studies have shown that the two hallmark topological codes---the toric code and color codes---are stable against bit-flip/phase-flip and measurement errors. In this work we study the effects of the depolarizing channel to both the toric code and topological color codes. By mapping the quantum problem onto a disordered statistical-mechanical 8-vertex model we compute the error tolerance of these systems using large-scale Monte Carlo simulations. Our results show that the error threshold increases significantly for both the toric code and color codes. [Preview Abstract] |
Friday, March 25, 2011 10:24AM - 10:36AM |
Y27.00013: Local equivalence of topological order: Kitaev's code and color codes Guillaume Duclos-Cianci, Hector Bombin, David Poulin We demonstrate that distinct topological codes can be mapped onto each other by local transformations. The existence of such a local mapping can be interpreted as saying that these codes belong to the same topological phase. When used as quantum error correcting codes, the local mapping also enables us to use any decoding algorithm suitable for one of these codes to decode other codes in the same topological phase. We illustrate this idea with the topological color code and the topological subsystem color code that are found to be locally equivalent to two copies of Kitaev's toric code. We are therefore able to decode these two codes that had no previously known efficient decoding algorithm, and find error thresholds comparable to previously estimated optimal values. These local mappings could have additional use for fault-tolerant quantum computation. In particular, one could in principle take advantage of the features (transversal gates, topological gates, etc.) of all the codes that are locally equivalent by switching between them during the computation in a fault-tolerant fashion. [Preview Abstract] |
Friday, March 25, 2011 10:36AM - 10:48AM |
Y27.00014: Exactly solvable 3D quantum model with finite temperature topological order Isaac Kim We present a family of exactly solvable spin-$\frac{1}{2}$ quantum hamiltonians on a 3D lattice. The degenerate ground state of the system is characterized by a quantum error correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models 1) have solely local interactions 2) admit a strong-weak duality relation with an Ising model on a dual lattice 3) have topological order in the ground state, some of which survive at finite temperature. The associated quantum error correcting codes are all non-CSS stabilizer codes. [Preview Abstract] |
Friday, March 25, 2011 10:48AM - 11:00AM |
Y27.00015: Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models Benjamin Hsu, Eduardo Fradkin We examine the scaling behavior of the entanglement entropy for the 2D quantum dimer model (QDM) at criticality and derive the universal finite sub-leading correction $\gamma_{QCP}$. We compute the value of $\gamma_{QCP}$ without approximation working directly with the wave function of a generalized 2D QDM at the Rokhsar-Kivelson QCP in the continuum limit. Using the replica approach, we construct the conformal boundary state corresponding to the cyclic identification of $n$-copies along the boundary of the observed region. We find that the universal finite term is $\gamma_{QCP}=\ln R-1/2$ where $R$ is the compactification radius of the bose field theory quantum Lifshitz model, the effective field theory of the 2D QDM at quantum criticality. We also demonstrated that the entanglement spectrum of the critical wave function on a large but finite region is described by the characters of the underlying conformal field theory. It is shown that this is formally related to the problems of quantum Brownian motion on $n$-dimensional lattices or equivalently a system of strings interacting with a brane containing a background electromagnetic field and can be written as an expectation value of a vertex operator. [Preview Abstract] |
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