Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session C44: Anyons, Tensor Networks and Quantum Walks |
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Sponsoring Units: GQI Room: 347 |
Monday, March 14, 2016 2:30PM - 2:42PM |
C44.00001: Universal Finite-Size Scaling around Topological Quantum Phase Transitions Tobias Gulden, Michael Janas, Yuting Wang, Alex Kamenev The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the behavior away from criticality and obtain a scaling function. In contrast to scaling functions for entanglement entropy it discriminates between phases with different topological indexes. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with non-trivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results. [Preview Abstract] |
Monday, March 14, 2016 2:42PM - 2:54PM |
C44.00002: Long-range mutual information and topological uncertainty principle Chao-Ming Jian, Isaac Kim, Xiao-Liang Qi Ordered phases in Landau paradigm can be diagnosed by a local order parameter, whereas topologically ordered phases cannot be detected in such a way. In this paper, we propose long-range mutual information (LRMI) as a unified diagnostic for both conventional long-range order and topological order. Using the LRMI, we characterize orders in n$+$1D gapped systems as m-membrane condensates with 0 $\le $ m $\le $ n-1. The familiar conventional order and 2$+$1D topological orders are respectively identified as 0-membrane and 1-membrane condensates. We propose and study the topological uncertainty principle, which describes the non-commuting nature of non-local order parameters in topological orders. [Preview Abstract] |
Monday, March 14, 2016 2:54PM - 3:06PM |
C44.00003: Systematically Generated Two-Qubit Braids for Fibonacci Anyons Daniel Zeuch, Caitlin Carnahan, N. E. Bonesteel We show how two-qubit Fibonacci anyon braids can be generated using a simple iterative procedure which, in contrast to previous methods, does not require brute force search [1]. Our construction is closely related to that of [2], but with the new feature that it can be used for three-anyon qubits as well as four-anyon qubits. The iterative procedure we use, which was introduced by Reichardt [3], generates sequences of three-anyon weaves that asymptotically conserve the total charge of two of the three anyons, without control over the corresponding phase factors. The resulting two-qubit gates are independent of these factors and their length grows as log 1/$\epsilon$, where $\epsilon$ is the error, which is asymptotically better than the Solovay-Kitaev method.\\ \ \ [1] C. Carnahan, D. Zeuch, and N. E. Bonesteel, arXiv:1511.00719v1 (2015).\\ \ [2] H. Xu and X. Wan, Phys. Rev. A \textbf{78}, 042325 (2008).\\ \ [3] B. W. Reichardt, Quantum Information & Computation \textbf{12}, 876 (2012). [Preview Abstract] |
Monday, March 14, 2016 3:06PM - 3:18PM |
C44.00004: Scaling and Topological Phase Transitions: Energy vs. Entropy Yuting Wang, Tobias Gulden, Michael Janas, Alex Kamenev The critical point of a topological phase transition is described by a conformal field theory. Finite-size corrections give rise to a scaling function away from criticality for both energy and entanglement entropy of the system. While in the past the scaling function for the usual von Neumann entropy was found to be equal for the trivial and the topological side of the transition, we find that the scaling functions for energy and Renyi entropy with $\alpha>1$ are different for the two sides. This provides an easy tool to distinguish between the trivial and topological phases near criticality. [Preview Abstract] |
Monday, March 14, 2016 3:18PM - 3:30PM |
C44.00005: Ising anyons at finite temperature Chris Self, James Wootton, Sofyan Iblisdir, Jiannis Pachos Topological quantum computing offers a robust approach to quantum computation using braiding and fusion of anyonic particles. A particular type of anyons called Ising anyons are known to emerge from the microscopics of a spin lattice model called the Kitaev honeycomb\footnote{A. Kitaev {Ann. Phys.} 321.1 (2006): 2-111.}$^{,}$\footnote{V. Lahtinen et al. {New J. Phys} 11.9 (2009): 093027.}. We study the Ising anyon phase of the Kitaev honeycomb at finite temperature using Monte Carlo methods. We find evidence of the thermal fractionalization of the spins into Majorana modes, similar to the recent results of \footnote{J. Nasu et al. {arXiv}:1504.01259 (2015)} who studied the non-Ising anyon phases of the model. We relate these findings to the finite temperature stability of the topological characteristics of the model. In addition we probe the thermal edge currents of the Kitaev honeycomb. Analogy to conformal field theory suggests that if the system has a boundary then at very low temperatures there should be a chiral edge current along that boundary that scales with $T^2$. By defining a microscopic current operator and taking its finite temperature expectation value we demonstrate edge currents that obey this scaling. [Preview Abstract] |
Monday, March 14, 2016 3:30PM - 3:42PM |
C44.00006: Robust Topological and Holographic Degeneracies of Classical Systems Seyyed Mohammad Sadegh Vaezi, Zohar Nussinov, Gerardo Ortiz We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that in certain lattice realizations of these models, and other theories, one can find a ground state entropy that is "holographic", i.e., extensive in the system's boundary. [Preview Abstract] |
Monday, March 14, 2016 3:42PM - 3:54PM |
C44.00007: Topological defects on the lattice David Aasen, Roger Mong, Paul Fendley We construct defects in two-dimensional classical lattice models and one-dimensional quantum chains that are topologically invariant in the continuum limit. We show explicitly that these defect lines and their trivalent junctions commute with the transfer matrix/Hamiltonian. The resulting splitting and joining properties of the defect lines are exactly those of anyons in a topological phase. One useful consequence is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization, and so provide a natural way of relating microscopic and macroscopic properties. Another is a generalization of Kramers-Wannier duality to a wide class of height models. Even more strikingly, we derive the modular transformation matrices explicitly and exactly from purely lattice considerations. We develop this construction for a variety of examples including the two-dimensional Ising model. [Preview Abstract] |
Monday, March 14, 2016 3:54PM - 4:06PM |
C44.00008: How quickly can anyons be braided? Christina Knapp, Dong Liu, Meng Cheng, Michael Zaletel, Parsa Bonderson, Chetan Nayak Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature. However, it is less well-understood how error rates depend on the speed with which anyons are braided. In general, diabatic corrections to the Berry phase vanish inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. Here, we show that such corrections will not affect quantum information encoded in a topological state unless topologically non-trivial quasiparticles are created. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error. [Preview Abstract] |
Monday, March 14, 2016 4:06PM - 4:18PM |
C44.00009: Edge theory approach to topological entanglement entropy and other entanglement measures of (2+1) dimensional Chern-Simons theories on a general manifold Xueda Wen, Shunji Matsuura, Shinsei Ryu Topological entanglement entropy of (2+1) dimensional Chern-Simons gauge theories on a general manifold is usually calculated with Witten’s method of surgeries and replica trick, in which the spacetime manifold under consideration is very complicated. In this work, we develop an edge theory approach, which greatly simplifies the calculation of topological entanglement entropy of a Chern-Simons theory. Our approach applies to a general manifold with arbitrary genus. The effect of braiding and fusion of Wilson lines can be straightforwardly calculated within our framework. In addition, our method can be generalized to the study of other entanglement measures such as mutual information and entanglement negativity of a topological quantum field theory on a general manifold. [Preview Abstract] |
Monday, March 14, 2016 4:18PM - 4:30PM |
C44.00010: Highly entangled tensor networks Yingfei Gu, Daniel Bulmash, Xiao-Liang Qi Tensor network states are used to represent many-body quantum state, e.g., a ground state of local Hamiltonian. In this talk, we will provide a systematic way to produce a family of highly entangled tensor network states. These states are entangled in a special way such that the entanglement entropy of a subsystem follows the Ryu-Takayanagi formula, i.e. the entropy is proportional to the minimal area geodesic surface bounding the boundary region. Our construction also provide an intuitive understanding of the Ryu-Takayanagi formula by relating it to a wave propagation process. We will present examples in various geometries. [Preview Abstract] |
Monday, March 14, 2016 4:30PM - 4:42PM |
C44.00011: Tensor network characterization of superconducting circuits Guillaume Duclos-Cianci, David Poulin, Alireza Najafi-Yazdi Superconducting circuits are promising candidates in the development of reliable quantum computing devices. In principle, one can obtain the Hamiltonian of a generic superconducting circuit and solve for its eigenvalues to obtain its energy spectrum. In practice, however, the computational cost of calculating eigenvalues of a complex device with many degrees of freedom can become prohibitively expensive. In the present work, we investigate the application of tensor network algorithms to enable efficient and accurate characterization of superconducting circuits comprised of many components. Suitable validation test cases are performed to study the accuracy, computational efficiency and limitations of the proposed approach. [Preview Abstract] |
Monday, March 14, 2016 4:42PM - 4:54PM |
C44.00012: Direct Measurement of Topological Phases in Discrete-Time Quantum Walks: Theory Vinay Ramasesh, Emmanuel Flurin, Irfan Siddiqi, Norman Yao Quantum walks have been intently investigated theoretically, from initial studies motivated by their connection to classical randomized algorithms to more recent works demonstrating topological phenomena in these walks. In particular, quantum walks simulate dynamics under effective lattice Hamiltonians which feature spin-orbit coupling. Here, we demonstrate that by adding an additional coin operator which varies from step to step, one can perform a traversal of the effective Brillouin zone, analogous to a Bloch oscillation. The geometric phase picked up by the walker along the Bloch oscillation is a genuine signature of the walk’s topology, a quantity known in 1D as the Zak phase. Unlike previous interferometric proposals, our work requires neither spin-dependent Ramsey spectroscopy nor an external impurity with additional degrees of freedom. We develop a protocol, illustrating its use in a circuit QED system, which allows for the detection of the Zak phase. [Preview Abstract] |
Monday, March 14, 2016 4:54PM - 5:06PM |
C44.00013: Direct Measurement of Topological Phases in Discrete-Time Quantum Walks - Experiment Emmanuel Flurin, Vinay V Ramasesh, Shay Hacohen Gourgy, Norman Y Yao, Irfan Siddiqi We perform quantum walks in a cavity QED architecture. Here a transmon qubit plays the role of the quantum coin, while a set of coherent states in an electromagnetic cavity forms the walker’s lattice. The strong dispersive coupling between the transmon and cavity naturally implements coin-dependent translations of the walker state. The walk is performed by applying qubit rotations at equally spaced intervals; interestingly, such systems simulate dynamics under effective lattice Hamiltonians which feature strong spin-orbit coupling, leading to non-trivial band topology. By adding an additional step-dependent coin operator, we perform the first direct measurement of a quantum walk Zak phase, delineating between topologically trivial and non-trivial walks. The geometric phase is detected by implementing the quantum walk with the initial state of the walker in a superposition of a coherent state and the vacuum state, which does not partake in the walk. The Zak phase acquired by the walker thus leaves an imprint in the interference fringes of the resulting Schrodinger cat state. We observe these fringes by directly measuring the cavity Wigner function. [Preview Abstract] |
Monday, March 14, 2016 5:06PM - 5:18PM |
C44.00014: On the physical realizability of quantum stochastic walks Bruno Taketani, Luke Govia, Peter Schuhmacher, Frank Wilhelm Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks. [Preview Abstract] |
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