Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session A07: Topological Quantum Information and Computation |
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Sponsoring Units: DQI Chair: Mercedes Gimeno-Segovia, University of Bristol Room: LACC 153B |
Monday, March 5, 2018 8:00AM - 8:12AM |
A07.00001: Anyonic Entanglement and Topological Entanglement Entropy Christina Knapp , Parsa Bonderson , Kaushal Patel We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy. |
Monday, March 5, 2018 8:12AM - 8:24AM |
A07.00002: Topological Entanglement Entropy in Euclidean AdS_{3} via Surgery Haoyu Sun , Zhuxi Luo We calculate the topological entanglement entropy (TEE) in Euclidean asymptotic AdS_{3} spacetime using surgery. Bipartiting along the horizon of the eternal BTZ black hole, we get TEE exactly matching the Bekenstein-Hawking entropy, which supports the ER=EPR conjecture in the Euclidean bulk. After summing partition functions over genus-one classical geometries, we compute TEE at high-temperature. In the case with the most negative global curvature, we find that TEE equals that of the Moonshine double state, given by the maximally-entangled superposition of 194 types of “anyons” in the bulk, labeled by irreducible representations of the Monster group. We propose this as the bulk analog of the thermofield double state in the Euclidean AdS_{3}. |
Monday, March 5, 2018 8:24AM - 8:36AM |
A07.00003: Entanglement entropy of (3+1)D topological orders with excitations Xueda Wen , Huan He , Apoorv Tiwari , Yunqin Zheng , Peng Ye Excitations in (3+1)D topologically ordered phases have very rich structures. (3+1)D topological phases support both point-like and string-like excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the question how different types of topological excitations contribute to the entanglement entropy, or alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological orders? We are mainly interested in (3+1)D topological orders that can be realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite group $G$ and its group 4-cocycle $\omega\in\mathcal{H}^4[G;U(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant $\log d_i$ to the entanglement entropy, where $d_i$ is the quantum dimension that depends on both the structure of the excitation and the data $(G,\,\omega)$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\,\omega)$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\omega$ from the others. |
Monday, March 5, 2018 8:36AM - 8:48AM |
A07.00004: Symmetry-Enriched Topological Order in Tensor Networks Dominic Williamson , Nick Bultinck , Frank Verstraete We have studied symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion categories was established. Tensor network representations of the topological defect superselection sectors were constructed for all domain walls. The emergent symmetry-enriched topological order was extracted from these representations, including the symmetry action on the underlying anyons. Dual phase transitions, induced by gauging a global symmetry, and condensation of a bosonic subtheory, were analyzed and the relationship between topological orders on either side of the transition were derived. |
Monday, March 5, 2018 8:48AM - 9:00AM |
A07.00005: Entanglement properties of the time periodic Kitaev Chain Daniel Yates , Aditi Mitra The entanglement properties of the time periodic Kitaev chain with nearest neighbor and next nearest neighbor hopping, is studied. The cases of the exact eigenstate of the time periodic Hamiltonian, referred to as the Floquet ground state (FGS), as well as a physical state obtained from time-evolving an initial state unitarily under the influence of the time periodic drive are explored. Topological phases are characterized by different numbers of Majorana zero (Z_0) and π (Z_π) modes, where the zero modes are present even in the absence of the drive, while the π modes arise due to resonant driving. The entanglement spectrum (ES) of the FGS as well as the physical state show topological Majorana modes whose number is different from that of the quasi-energy spectrum. The number of Majorana edge modes in the ES of the FGS vary in time from |Z_0-Z_π| to Z_0+Z_π within one drive cycle, with the maximal Z_0+Z_π modes appearing at a special time-reversal symmetric point of the cycle. For the physical state on the other hand, only the modes inherited from the initial wavefunction, namely the Z_0 modes, appear in the ES. The Z_π modes are absent in the physical state as they merge with the bulk excitations that are simultaneously created due to resonant driving. |
Monday, March 5, 2018 9:00AM - 9:12AM |
A07.00006: Time correlations and Leggett-Garg inequalities for probing the topological phase transition in the Kitaev chain Luis Quiroga , Fernando Gómez-Ruiz , Juan Mendoza-Arenas , Ferney Rodríguez , Carlos Tejedor Topological states (TS) in the Kitaev chain have shown as robust quantum information entities with potential applications in topological quantum computation protocols. A major challenge in these new proposals is the control of both the autonomous as well as directed time evolution of TS, an issue rather unexplored up to now. We evaluate the interplay between time dependent quantum correlations and nonlocal quantum objects such as Majorana based qubits. We use two-time correlations (TTC) and Leggett-Garg inequalities (LGI) for identifying the transition between normal and the topological phase in a Kitaev chain. TTC and LGI of dichotomic quantum observables associated with fermion occupation number of both local as well as nonlocal qubit operators (formed by pairing local and non-local Majorana fermions) are analyzed for different chain lengths and chemical potentials. In order to gain further insight on the physical properties of the system's dynamics, violations of LGI are also evaluated for different string order parameter qubits. We obtain analytical results which allow us to understand the fundamental aspects of TTC in topological Kitaev chains. |
Monday, March 5, 2018 9:12AM - 9:24AM |
A07.00007: Majorana qubit readout using parametric modulation of light-matter coupling Arne Grimsmo , Alexandre Blais , Karl Petersson Logical readout of Majorana qubits is a key primitive in approaches to topological quantum computing based on Majorana zero modes. The qubit readout protocol should be fast, high fidelity and, ideally, quantum non-demolition. The readout scheme should also be scalable and involve minimal device complexity. We present a readout protocol that is promising with respect to all these desiderata. The measurement is based on parametric modulation of the light-matter coupling between a microwave resonator and a pair of overlapping Majorana wave-functions. |
Monday, March 5, 2018 9:24AM - 9:36AM |
A07.00008: Realistic numerical modeling of topological qubits John Gamble , Jan Gukelberger , Donjan Rodic , Kevin Van Hoogdalem , Andrey Antipov , Fabrizio Nichele , Asbjørn Drachmann , Alexander Whiticar , Eoin O'Farrell , Antonio Fornieri , Charles Marcus , Matthias Troyer Using the Majorana zero modes of one-dimensional systems as topological qubits has recently generated considerable interest, with experimental efforts progressing rapidly, necessitating increasingly intricate qubit encoding schemes and layouts. Moving from a sketch of a complex design to a physical layout is a daunting engineering challenge, as small details of the design can have large impacts on device operation. Here, we present a computational tool chain that simulates the physics of these devices from the CAD schematics used for fabrication. By systematically varying the designs, we perform high-throughput computations to probe vast swaths of design space. Our simulations take into account the physical effects of self-consistent screening and superconductivity, while also including the detailed geometric configurations and fringing fields that are critical to device performance. Finally, we show validation comparisons with recent experiments in InAs gate-defined nanowire systems. |
Monday, March 5, 2018 9:36AM - 9:48AM |
A07.00009: InAsSb Quantum Wells for Topological Quantum Computation Mihir Pendharkar , Joon Sue Lee , Chris Palmstrom Recent advances in coupling superconductivity to near surface InAs quantum wells (QWs) have allowed for the first observation of Majorana Zero Modes on a scalable platform paving the way for lithographically defined complex networks necessary for topological quantum computation. Increase in spin-orbit coupling should lead to an increase in induced topological gap and topological protection. InAsSb may have a higher spin-orbit coupling than both InAs and InSb. In this work, near surface InAs(x)Sb(1-x) quantum wells, with varying As/Sb ratio and varying depth from the surface have been demonstrated. Formation of a near surface 2DEG in InAs is aided by presence of a surface accumulation layer, while Fermi level pinning within the band gap of InSb inhibits this. As/Sb ratio in InAsSb can in principle be used to tune the surface pinning. Magneto-transport of InAs(0.2)Sb(0.8) QWs at 2K indicates the presence of a surface depletion layer deduced by a reduction in dopant ionization efficiency with reducing depth from the surface. This work is expected to aid in providing a direct control over the coupling of superconductivity from an in-situ grown epitaxial Aluminum layer through a ‘tuned’ tunnel barrier while setting up a new platform for robust induced topological superconductivity. |
Monday, March 5, 2018 9:48AM - 10:00AM |
A07.00010: Dephasing of Charging-Energy-Protected Majorana Zero Mode Qubits Torsten Karzig , Christina Knapp , Roman Lutchyn , Chetan Nayak We analyze charging-energy-protected Majorana zero mode (MZM) qubits, focusing on the residual dephasing that is present when the distance between MZMs is insufficient for full topological protection. We argue that the leading source of dephasing is $1/f$ charge noise. This noise affects the qubit as a result of the hybridization energy and charge distribution associated with weakly-overlapping MZMs, which we calculate using a charge-conserving formalism. In contrast to mean-field descriptions, the latter emphasizes that a finite MZM overlap leads to the formation of a charge dipole rather than an absolute charge build-up. We estimate the coherence time to be of the order of a hundred nanoseconds for MZM qubits whose MZM separation is $L\sim 5\xi$ (with $\xi$ being the coherence length). The coherence time grows exponentially with MZM separation and eventually becomes temperature-limited, reaching values of the order of minutes for $L/\xi \sim 30$. |
Monday, March 5, 2018 10:00AM - 10:12AM |
A07.00011: Symmetry-protected metrology with the Haldane phase Gavin Brennen , Stephen Bartlett , Akiwasa Miyake One of the challenges of using a quantum sensor to achieve enhanced measurement precision is that the very properties of entangled states that makes a sensor sensitive to a field also makes it sensitive to unwanted noise. Active error correction can overcome some of this but at the cost of complicated control sequences and/or knowlege of the direction of the field. |
Monday, March 5, 2018 10:12AM - 10:24AM |
A07.00012: Spectral Analysis of Loschmidt Echo in Nuclear Spin Baths Ekrem Güldeste , Ceyhun Bulutay The revivals of the background spins coupled to a qubit constitute Loschmidt echo which plays a crucial role in the storage of quantum information within a solid-state matrix. Its characterization and quantum control are currently of wide interest. Here, we present the spectral analysis of Loschmidt echo in a nuclear spin bath. The model spin-Hamiltonian consists of both hyperfine and quadrupolar couplings together with nearest-neighbor two-body interactions. For this so-called central spin problem, we use the exact diagonalization for small spin systems, and for the larger ones we resort to the cluster correlation expansion technique. Predominantly through the hyperfine term, a feedback loop is formed which introduces nonlinearity and harmonics into the system. Our Fourier analysis of the Loschmidt echo sheds light on how the spectral profile is synthesized through various interactions. This provides an invaluable insight on the qubit decoherence and control of the nuclear spin reservoir. |
Monday, March 5, 2018 10:24AM - 10:36AM |
A07.00013: Experimental Solid State Quantum Simulation Using 1D Superlattice Structures Megan Briggeman , Mengchen Huang , Anthony Tylan-Tyler , Jungwoo Lee , Hyungwoo Lee , Chang-Beom Eom , Patrick Irvin , Jeremy Levy Quantum systems exhibit behavior that is difficult to model. One approach is to use configurable quantum systems in which the Hamiltonian can be mapped onto the system of interest. This approach, known as quantum simulation, requires a rich system whose quanta and interactions can be controlled precisely, at the level of single electrons and other degrees of freedom. Here we describe steps toward developing a quantum simulation platform using the complex oxide heterostructure LaAlO_{3}/SrTiO_{3} by creating systems with features comparable to the mean spacing between electrons. The interface has strong, sign changing, gate-tunable e-e interactions that can influence the quantum ground state. We explore magnetotransport of 1D superlattices, where periodic modulation produces dispersive features not seen in control devices. These results can be compared with effective 1D model Hamiltonians to bridge experiment and theory and enable quantum simulation of more complex systems. |
Monday, March 5, 2018 10:36AM - 10:48AM |
A07.00014: Quantum Hall plasmonics for quantum computation Stefano Bosco , David DiVincenzo Quantum Hall edge plasmons have some characteristic features that can be useful to measure and control solid state qubits. For example, it was recently demonstrated that their chirality can be exploited to implement passive non-reciprocal devices, such as gyrators and circulators, that exhibit good scalability performance. The improved scalability is related to the high ratio between the transverse voltage and the current, which is typical of the quantum Hall effect. Since the velocity of the edge excitations is inversely proportional to this ratio, shorter wavelengths have higher frequencies than in usual microwave devices. This high off-diagonal resistance can also be exploited to implement nearly dissipationless transmission lines and resonators with high characteristic impedance. This talk will focus on the latest theoretical developments on this topic. Different ways to implement these plasmonic transmission lines, e.g. with distributed or lumped elements, will be discussed and a quantitative analysis of different coupling schemes to semiconducting qubits will be presented. |
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