Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session A44: Quantum Information with Majorana Fermions & Parafermions |
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Sponsoring Units: GQI Chair: David Aasen, California Institute of Technology Room: 347 |
Monday, March 14, 2016 8:00AM - 8:12AM |
A44.00001: Milestones toward Majorana-based quantum computing: Fusion rule detection and topological qubit validation Ryan V. Mishmash, David Aasen, Michael Hell, Andrew Higginbotham, Jeroen Danon, Martin Leijnse, Thomas S. Jespersen, Joshua A. Folk, Charles M. Marcus, Karsten Flensberg, Jason Alicea We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires coated with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate-control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. Recently, we have outlined a sequence of relatively modest milestones which interpolate between zero-mode detection and longer term quantum computing applications. In this talk, I will discuss two of these milestones: (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensing or Majorana-mediated charge pumping and (2) validation of a prototype topological qubit via unconventional scaling relations between the time-averaged qubit splitting and its decoherence times $T_1$ and $T_2$. Both of these proposed experiments require only a single wire with two islands---a hardware configuration already available in the laboratory. Furthermore, these pre-braiding experiments can be adapted to other manipulation and readout schemes as well. [Preview Abstract] |
Monday, March 14, 2016 8:12AM - 8:24AM |
A44.00002: Gate-controlled charging effects in superconducting nanowires: low-energy spectrum and time scales for Majorana manipulation Michael Hell, Jeroen Danon, Martin Leijnse, Karsten Flensberg In this talk, we investigate the gate-controlled crossover between different operating regimes of a superconducting nanowire segmented into two islands each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could be realized in the near future as a platform for testing Majorana fusion rules. We present a numerical study of the low-energy spectrum of this device covering both the charge-dominated regime utilizable for initialization and readout of the Majorana bound states as well as the Josephson-dominated transmon regime allowing for Majorana manipulations. Depending on the relative size of the energy scales associated with the Majorana coupling, the charging energy, and the transmon frequency, the „fine structure“ of the low-energy spectrum differs. We finally discuss the associated time scales for implementing a fusion-rule testing protocol discussed in the talks by J. Alicea and R. V. Mishmash. [Preview Abstract] |
Monday, March 14, 2016 8:24AM - 8:36AM |
A44.00003: Demonstrating non-Abelian statistics of Majorana fermions using twist defects Huaixiu Zheng, Arpit Dua, Liang Jiang We study the twist defects in the toric code model introduced by Bombin [Phys. Rev. Lett.105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner transformation and a projective construction, we show explicitly the twist defects carry unpaired Majorana zero modes. In addition, we propose a quantum non-demolition measurement scheme of the parity of Majorana modes. Such a scheme provides an alternative avenue to demonstrate the non-Abelian statistics of Majorana fermions. The braiding operation is simulated by an efficient measurement-based approach that removes the uncertainty associated with the previous forced measurement scheme. [Preview Abstract] |
Monday, March 14, 2016 8:36AM - 8:48AM |
A44.00004: Parafermions in spin lattices Arpit Dua, Huaixiu Zheng, Liang Jiang We investigate the twist defects in the Z$_{N}$ Toric code model first introduced by Bombin [Phys. Rev. Lett.105, 030403 (2010)] for the Z$_{2}$ model and then generalized and studied by You et al. [Phys. Rev. B 86, 161107(R) (2012)]. Using topological entanglement entropy (TEE) and generalized Jordan-Wigner transformation, we show explicitly that the twist defects carry unpaired Parafermion zero modes. We also demonstrate the fusion rules of these Parafermion modes using the TEE calculation. In addition, we propose a scheme for quantum non-demolition measurement of the topological charge of these modes. This scheme can be used to implement measurement-based braidings (MBBs) on Parafermions to implement gates for quantum computing. [Preview Abstract] |
Monday, March 14, 2016 8:48AM - 9:00AM |
A44.00005: Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes Shu-Ping Lee, Roman M. Lutchyn, Joseph Maciejko Odd-frequency superconductivity, originally proposed by Berezinskii in 1974, is an exotic phase of matter in which pairing is entirely dynamical in nature. The pair potential is an odd function of frequency, leading to a vanishing static superconducting order parameter and exotic types of pairing seemingly inconsistent with Fermi statistics, such as spin triplet (singlet) pairing in an s-wave (p-wave) superconductor. Motivated by recent experimental progress in the realization of Majorana zero modes in semiconducting nanowires, we show that a spin-polarized nanowire coupled to a one-dimensional array of Majorana zero modes becomes an odd-frequency superconductor. [Preview Abstract] |
Monday, March 14, 2016 9:00AM - 9:12AM |
A44.00006: Readout scheme for Majorana parity states using a quantum dot Darryl Hoving, Kaveh Gharavi, Jonathan Baugh We propose and numerically study a scheme for reading out the parity state of a pair of Majorana bound states using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be controlled by changing the position of the spatially separated, uncoupled MBS via a set of keyboard gates. Our simulations show that the oscillatory nature of the MBS splitting versus separation does not prevent high-fidelity readout. Indeed, the scheme can also be applied to measure the splitting versus separation, which would yield a clear signature of the topological state. With experimentally realistic parameters we find parity readout fidelities $>$99\% should be feasible. [Preview Abstract] |
Monday, March 14, 2016 9:12AM - 9:24AM |
A44.00007: Majorana Fermion Rides on a Magnetic Domain Wall Se Kwon Kim, Sumanta Tewari, Yaroslav Tserkovnyak Owing to the recent progress on endowing the electronic structure of magnetic nanowires with topological properties, the associated topological solitons in the magnetic texture---magnetic domain walls---appear as very natural hosts for exotic electronic excitations. Here, we propose to use the magnetic domain walls to engender Majorana fermions [1], which has several notable advantages compared to the existing approaches. First of all, the local tunneling density-of-states anomaly associated with the Majorana zero mode bound to a smooth magnetic soliton is immune to most of parasitic artifacts associated with the abrupt physical ends of a wire, which mar the existing experimental probes. Second, a viable route to move and braid Majorana fermions is offered by domain-wall motion. In particular, we envision the recently demonstrated heat-current induced motion of domain walls in insulating ferromagnets as a promising tool for nonintrusive displacement of Majorana modes. This leads us to propose a feasible scheme for braiding domain walls within a magnetic nanowire network, which manifests the nob-Abelian exchange statistics within the Majorana subspace. \\ [4pt] [1] S. K. Kim, S. Tewari, and Y. Tserkovnyak, Phys. Rev. B \textbf{92}, 020412(R) (2015) \\ [Preview Abstract] |
Monday, March 14, 2016 9:24AM - 9:36AM |
A44.00008: Majorana Fermion Surface Code for Universal Quantum Computation Sagar Vijay, Tim Hsieh, Liang Fu We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_{2}$ topological order with a $Z_{2}$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by $s$-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations. [Preview Abstract] |
Monday, March 14, 2016 9:36AM - 9:48AM |
A44.00009: Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires Jay Sau, Maissam Barkeshli The idea of topological quantum computation (TQC) is to encode and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, the most promising platforms for a topological qubit are either in terms of Majorana fermion zero modes (MZMs) in spin-orbit coupled superconducting nanowires or in terms of the Kitaev Z2 surface code. However, the topologically robust operations that are possible in these systems are not sufficient for realizing a universal gate set for topological quantum computation. Here, we show that an array of coupled semiconductor/superconductor nanowires with MZM edge states can be used to realize a more sophisticated type of non-Abelian defect, a genon in an Ising X Ising topological state. This leads to a possible implementation of the missing topologically protected pi/8 phase gate and thus paves a path for universal topological quantum computation based on semiconductor-superconductor nanowire technology. We provide detailed numerical estimates of the relevant energy scales, which we show to lie within accessible ranges. [1] Barkeshli, Sau, arXiv:1509.07135 (2015). [Preview Abstract] |
Monday, March 14, 2016 9:48AM - 10:00AM |
A44.00010: Braiding Majorana fermions in p+ip superfluids with particle number conservation Yiruo Lin, Anthony Leggett We discuss braiding statistics of Majorana zero modes localized in vortices in 2D spinless p+ip superfluids with conserved total particle number. In the standard particle non-conserved context, it has been argued that braiding these zero Majorana fermions yields non-abelian statistics. With particle number conservation, We show that in certain geometry, the Berry phase of interchanging two Majorana zero modes is proportional to angular momentum of the system with the presence of two vortices, which can then be calculated in the thermodynamic limit. The braiding statistics turns out to be consistent with the standard result. We then discuss the possible complication due to finite size effect. We'll argue that in a finite size system, the abelian phase of interchanging two vortices is non-topological. We'll finish the discussion by sketching out ongoing work in which we investigate the possible modification of BdG quasi-particle wave functions beyond the BdG mean-field approximation, which can have dramatic effect on topological properties of Majorana zero modes and their braiding statistics. [Preview Abstract] |
Monday, March 14, 2016 10:00AM - 10:12AM |
A44.00011: Beyond parafermions: Defects and zero-modes in non-Abelian phases Netanel Lindner, Erez Berg, Ady Stern Non-Abelian topological phases of matter can be utilized to encode and manipulate quantum information in a non-local manner, such that it is protected from imperfections in the implemented protocols and from interactions with the environment. The condition that the non-Abelian statistics of the anyons supports a computationally universal set of gates sets a very stringent requirement which is not met by many topological phases. We consider the possibility to enrich the possible topological operations supported by a non-Abelian topological phase by introducing defects into the system. We show that such defects bind zero modes which form a unique algebra that goes beyond the algebra of parafermions which describes defects in Abelian phases. For the case of a bi-layer containing Ising anyons, we show that by coupling zero modes one can obtain a set of topological operations that implements a universal set of gates. [Preview Abstract] |
Monday, March 14, 2016 10:12AM - 10:24AM |
A44.00012: Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires Chun Chen, Fiona Burnell Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practise this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the timescales over which information is topologically protected. In this Letter we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-$1$D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall $($FQH$)$ edges. We show that, like $1$D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a $($dual$)$ quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential. [Preview Abstract] |
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