Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session A38: Focus Session: Topological Quantum Information |
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Sponsoring Units: GQI Chair: Mohammad Hafezi, University of Maryland Room: 212B |
Monday, March 2, 2015 8:00AM - 8:36AM |
A38.00001: Protected gates for topological quantum field theories Invited Speaker: Robert Koenig We give restrictions on the locality-preserving unitary automorphisms U, which are protected gates, for topologically ordered systems. For arbitrary anyon models, we show that such unitaries only generate a finite group, and hence do not provide universality. For abelian anyon models, we find that the logical action of U is contained in a proper subgroup of the generalized Clifford group. In the case D(?2), which describes Kitaev's toric code, this represents a tightening of statement previously obtained within the stabilizer framework (PRL 110:170503). For non-abelian models, we find that such automorphisms are very limited: for example, there is no non-trivial gate for Fibonacci anyons. For Ising anyons, protected gates are elements of the Pauli group. These results are derived by relating such automorphisms to symmetries of the underlying anyon model: protected gates realize automorphisms of the Verlinde algebra. We additionally use the compatibility with basis changes to characterize the logical action. This is joint work with M. Beverland, F. Pastawski, J. Preskill and S. Sijher. [Preview Abstract] |
Monday, March 2, 2015 8:36AM - 8:48AM |
A38.00002: Majorana Zero Modes Without Superconductivity at the Edge of Chiral Gapless Abelian Quantum Hall States Jennifer Cano, Meng Cheng, Maissam Barkeshli, Chetan Nayak We show that the $\nu=8$ integer quantum Hall state can support Majorana fermion zero modes at domain walls between its two different stable chiral edge phases, even without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations -- all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. The zero modes survive the presence of gapless fermions in the conventional edge phase. Remarkably, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states. [Preview Abstract] |
Monday, March 2, 2015 8:48AM - 9:00AM |
A38.00003: Fidelity of Majorana-based quantum operations Mostafa Tanhayi Ahari, Gerardo Ortiz, Babak Seradjeh It is well known that one-dimensional p-wave superconductor, the so-called Kitaev model, has topologically distinct phases that are distinguished by the presence of Majorana fermions. Owing to their topological protection, these Majorana fermions have emerged as candidates for fault-tolerant quantum computation. They furnish the operation of such a computation via processes that produce, braid, and annihilate them in pairs. In this work we study some of these processes from the dynamical perspective. In particular, we determine the fidelity of the Majorana fermions when they are produced or annihilated by tuning the system through the corresponding topological phase transition. For a simple linear protocol, we derive analytical expressions for fidelity and test various perturbative schemes. For more general protocols, we present exact numerics. Our results are relevant for the operation of Majorana-based quantum gates and quantum memories. [Preview Abstract] |
Monday, March 2, 2015 9:00AM - 9:12AM |
A38.00004: Strongly interacting Majorana fermions Marcel Franz, Ching-Kai Chiu, Dmitry Pikulin Interesting phases of quantum matter often arise when the constituent particles -- electrons in solids -- interact strongly. Such strongly interacting systems are however quite rare and occur only in extreme environments of low spatial dimension, low temperatures or intense magnetic fields. Here we introduce a new system in which the fundamental electrons interact only weakly but the low energy effective theory is described by strongly interacting Majorana fermions. The system consists of an Abrikosov vortex lattice in the surface of a strong topological insulator and is accessible experimentally using presently available technology. The simplest interactions between the Majorana degrees of freedom exhibit an unusual nonlocal structure that involves four distinct Majorana sites. We formulate simple lattice models with this type of interaction and find exact solutions in certain physically relevant one- and two-dimensional geometries. In other cases we show how our construction allows for the experimental realization of interesting spin models previously only theoretically contemplated. [Preview Abstract] |
Monday, March 2, 2015 9:12AM - 9:24AM |
A38.00005: An experimental proposal to observe non-abelian statistics of Majorana-Shockley fermions in an optical lattice Dong-Ling Deng, Sheng-Tao Wang, Kai Sun, Lu-Ming Duan Besides the conventional bosons and fermions, in synthetic two-dimensional (2D) materials there could exist more exotic quasi-particles with non-abelian statistics, meaning that the quantum states in the system will be transformed by non-commuting unitary operators when we adiabatically braid the particles one around another. The search for such non-abelian particles is of critical significance in the current investigation on quantum physics. Despite the recent great progress, it remains technically elusive to braid the quasi-particles in materials to verify their conjectured non-abelian statistics. Here, we propose an experimental scheme to observe non-abelian statistics with cold atoms in a 2D optical lattice. We show that the Majorana-Schockley modes associated with line defects can be braided with non-abelian statistics through adiabatic shift of the local potentials. Observation of the non-abelian statistics is of both fundamental interest and practical importance, in particular for topological quantum computation. [Preview Abstract] |
Monday, March 2, 2015 9:24AM - 9:36AM |
A38.00006: Decoherence Patterns of Topological Qubits from Majorana Modes Sung Po Chao, Shih Hao Ho, Chung Hsien Chou, Feng Li Lin We investigate the decoherence patterns of topological qubits in contact with the environment. Each topological qubit is made of two Majorana modes of a 1D Kitaev's chain. These two Majorana modes weakly interact with the fermionic/bosonic environments. We find the topological qubits decohere completely in the Ohmic and sub-Ohmic environments but not in the super-Ohmic ones. Though the fermion parities of the topological qubits cannot prevent the qubit states from decoherence in the sub-Ohmic environments, it can prevent the qubits turning into Gibbs state. We also study the cases in which each Majorana mode couples to different Ohmic-like environments and the time dependence of concurrence for two topological qubits. [Preview Abstract] |
Monday, March 2, 2015 9:36AM - 9:48AM |
A38.00007: A simple quasi-1D model of Fibonacci anyons David Aasen, Roger Mong, David Clarke, Jason Alicea, Paul Fendley There exists various ways of understanding the topological properties of Ising anyons---from simple free-fermion toy models to formal topological quantum field theory. For other types of anyons simple toy models rarely exist; their properties have to be obtained using formal self-consistency relations. We explore a family of gapped 1D local bosonic models that in a certain limit become trivial to solve and provide an intuitive picture for Fibonacci anyons. One can interpret this model as a quasi-1D wire that forms the building block of a 2D topological phase with Fibonacci anyons. With this interpretation all topological properties of the Fibonacci anyons become manifest including ground state degeneracy and braid relations. We conjecture that the structure of the model is protected by an emergent symmetry analogous to fermion parity. [Preview Abstract] |
Monday, March 2, 2015 9:48AM - 10:00AM |
A38.00008: Universal Quantum Computation From 2/3 Bilayer Quantum Hall States Abolhassan Vaezi, Maissam Barkeshli In this talk, I consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer, in the presence of interlayer tunneling. I show that interlayer tunneling can drive a continuous phase transition to an exotic non-Abelian state that contains the famous ``Fibonacci anyon,'' whose non-Abelian statistics is powerful enough for universal topological quantum computation. The analysis that I will present towards this result rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. The charge gap remains open at the phase transition while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at $\nu=2/3$ in bilayers, as past experiments may not have definitively ruled them out. \\[4pt] Reference: A. Vaezi, and M. Barkeshli, arXiv:1403.3383 (to appear in PRL) [Preview Abstract] |
Monday, March 2, 2015 10:00AM - 10:12AM |
A38.00009: Robust quantum control using smooth pulses and topological winding Edwin Barnes, Xin Wang Perhaps the greatest challenge in achieving control of microscopic quantum systems is the decoherence induced by the environment, a problem which pervades experimental quantum physics and is particularly severe in the context of solid state quantum computing and nanoscale quantum devices because of the inherently strong coupling to the surrounding material. We present an analytical approach to constructing intrinsically robust driving fields which automatically cancel the leading-order noise-induced errors in a qubit's evolution exactly. We address two of the most common types of non-Markovian noise that arise in qubits: slow fluctuations of the qubit energy splitting and fluctuations in the driving field itself. We demonstrate our method by constructing robust quantum gates for several types of spin qubits, including phosphorous donors in silicon and nitrogen-vacancy centers in diamond. Our results constitute an important step toward achieving robust generic control of quantum systems, bringing their novel applications closer to realization. [Preview Abstract] |
Monday, March 2, 2015 10:12AM - 10:24AM |
A38.00010: Measuring second Chern number from dynamics Michael Kolodrubetz, Tiago Souza, Anatoli Polkovnikov By using the fact that Berry curvature acts as an effective electromagnetic field, recent work has demonstrated the direct experimental measurement of the first Chern number in systems of one and two superconducting qubits. This basic idea should extend to a number of interesting cases, including the presence of finite temperature or degenerate ground states. In this talk, I will show how in such a system one can measure the next non-trivial number in a line of topological invariants -- the second Chern number. I will comment on experimental realizations of this measurement and its connection to fractionalization phenomena. [Preview Abstract] |
Monday, March 2, 2015 10:24AM - 10:36AM |
A38.00011: Topological Phases of Sound and Light Vittorio Peano Cavasola, Christian Brendel, Michael Schmidt, Florian Marquardt Topological states of matter are particularly robust, since they exploit global features insensitive to local perturbations. In this talk, we describe how to create a Chern insulator of phonons in the solid state. The proposed implementation is based on a simple setting, a dielectric slab with a suitable pattern of holes. Its topological properties can be wholly tuned in-situ by adjusting the amplitude and frequency of a driving laser that controls the optomechanical interaction between light and sound. The resulting chiral, topologically protected phonon transport along the edges can be probed completely optically. Moreover, we identify a regime of strong mixing between photon and phonon excitations, which gives rise to a large set of different topological phases. This would be an example of a Chern insulator produced from the interaction between two physically very different particle species, photons and phonons. [Preview Abstract] |
Monday, March 2, 2015 10:36AM - 10:48AM |
A38.00012: Topological Flux Phases of Levin-Wen String-Net Models Kaushal Patel, Parsa Bonderson, Kirill Shtengel, Steven Simon Levin-Wen string-net models provide exactly-solvable lattice models for gapped topological phases. We examine flux phases of these models, in which the lattice plaquettes contain a nontrivial flux instead of containing zero flux. In particular, we study $Z_N$ and Ising flux phases. We find that the Ising $\sigma$ flux phase is gapless, but nonetheless contains quasiparticles with topologically protected non-Abelian braiding statistics, thus providing an exactly-solvable model of a quasi-topological phase. [Preview Abstract] |
Monday, March 2, 2015 10:48AM - 11:00AM |
A38.00013: Critical entanglement spectrum of one-dimensional symmetry protected topological phases Guang-Ming Zhang, Xin Wan Under an appropriate symmetric extensive bipartition in a one-dimensional symmetry protected topological (SPT) phase, a bulk critical entanglement spectrum can be obtained, resembling the excitation spectrum of the critical point separating the SPT phase from the trivial (vacuum) state. Such a critical point is beyond the standard Landau Ginzburg-Wilson paradigm for symmetry breaking phase transitions. For the S=1 SPT (Haldane) phase with the Affleck-Kennedy-Lieb-Tasaki exact wave function, the resulting critical entanglement spectrum shows a delocalized version of the edge excitations in the SPT phase. From the wave function corresponding to the lowest entanglement energy level, the central charge of the critical point can be extracted and the critical theory can be identified as the same effective field theory as the spin-1/2 antiferromagnetic Heisenberg chain or the spin-1/2 Haldane-Shastry model with inverse square long-range interaction. (Reference: W. J. Rao, X. Wan, G. M. Zhang, Phys. Rev. B 90, 075151 (2014)) [Preview Abstract] |
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