Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session A07: Topological Quantum ComputingFocus

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Sponsoring Units: DQI Room: 102 
Monday, March 2, 2020 8:00AM  8:12AM 
A07.00001: Bifurcating entanglementrenormalization group flows of fracton stabilizer models Arpit Dua, Pratyush Sarkar, Dominic Williamson, Meng Cheng We investigate the entanglementrenormalization group flows of translationinvariant topological stabilizer models in three dimensions. Fracton models are observed to bifurcate under entanglement renormalization, generically returning at least one copy of the original model. Based on this behavior we formulate the notion of bifurcated equivalence for fracton phases, generalizing foliated fracton equivalence. The notion of quotient superselection sectors is also generalized accordingly. We calculate bifurcating entanglementrenormalization group flows for a wide range of examples and, based on those results, propose conjectures regarding the classification of translationinvariant topological stabilizer models in three dimensions. 
Monday, March 2, 2020 8:12AM  8:24AM 
A07.00002: Quantum electrodynamics in a topological metamaterial: Part 1 Eun Jong Kim, Xueyue Zhang, Alp Sipahigil, Vinicius S Ferreira, Jash Banker, Mohammad Mirhosseini, Oskar Painter The rich quantum electrodynamical properties arising from topological photonics open new possibilities for studying novel manybody states and implementing topologically protected quantum information processing protocols. It has been recently suggested that a topological waveguide, which realizes a photonic analog of the SuSchriefferHeeger (SSH) model, can host unconventional quantum optical phenomena [Sci. Adv. 5, eaaw0297 (2019)]. We discuss the implementation of the topological waveguide with superconducting metamaterials. We explore the exotic properties of qubitphoton bound states and topological edge states emergent in this system. 
Monday, March 2, 2020 8:24AM  8:36AM 
A07.00003: Quantum electrodynamics in a topological metamaterial: Part 2 Xueyue Zhang, Eun Jong Kim, Alp Sipahigil, Vinicius S Ferreira, Jash Banker, Mohammad Mirhosseini, Oskar Painter Topological concepts in photonics give rise to novel ways of controlling light or microwaves. By coupling quantum emitters to topological photonic structures, photonmediated interaction between the emitters inherits the topological properties, which can lead to novel radiative phenomena. Here, we study superconducting qubits coupled to a microwave metamaterial waveguide which is a photonic analog of the SuSchriefferHeeger (SSH) model [Sci. Adv. 5, eaaw0297 (2019)]. We report the observation of novel interaction profiles and scattering properties of the qubits induced by the topological photonic bath. 
Monday, March 2, 2020 8:36AM  8:48AM 
A07.00004: Transition from 2D to 1D topological superconductivity in a triangular island of pwave superconductor Aidan Winblad, Hua Chen

Monday, March 2, 2020 8:48AM  9:00AM 
A07.00005: Timeresolved electrical detection of chiral edge vortex braiding Inanc Adagideli, Fabian Hassler, Aurelien Grabsch, Michal Pacholski, Carlo W J Beenakker A $\bm{2\pi}$ phase shift across a Josephson junction in a topological 
Monday, March 2, 2020 9:00AM  9:12AM 
A07.00006: Braiding of Majorana Fermions in a Cavity Mircea Trif, Pascal Simon We study the dynamical process of braiding Majorana bound states (MBS) in the presence of the coupling to photons in a microwave cavity. We show theoretically that the π/4 phase associated with the braiding of MBS, as well as the parity of the ground state are imprinted into the photonic field of the cavity, which can be detected by dispersive readout techniques [1]. We use a density matrix description for the dynamics of the low energy states in order to account for various relaxation channels both in the adiabatic regime, as well as within the Floquet formalism in the case of periodic driving. We evaluate the average photon number and the second order photon coherence function g^{(2)}(0), and show they are affected by the non Abelian Berry phase accumulated during the braiding process [2]. These manifestations are purely dynamical, they occur in the absence of any splitting of the MBS that are exchanged, and they disappear in the static setups studied previously. Conversely, the cavity can affect the braiding phase, which in turn should allow for cavity controlled braiding. 
Monday, March 2, 2020 9:12AM  9:24AM 
A07.00007: Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure Xiaoyu Ma, Cynthia Reichhardt, Charles Reichhardt We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip. 
Monday, March 2, 2020 9:24AM  9:36AM 
A07.00008: Towards practical selfcorrection with augmented Majorana stabilizer codes Stephan Plugge, Marcel Franz, Robert Raussendorf, Ian Affleck We present design ideas for an augmented Majorana surface code (MSC) that allows improved errorcorrecting behavior on practically relevant timescales. The underlying mechanism resembles that of interacting anyon models, and facilitates the protected Hamiltonianlevel generation of stabilizer operators in MSCs together with coupling to auxiliary bosonic degrees of freedom. In this talk, I will discuss MSCs and their extensions affording improved errorcorrection, towards the goal of thermally stable quantum memories in 2D. 
Monday, March 2, 2020 9:36AM  9:48AM 
A07.00009: Optimizing Clifford gate generation for measurementonly topological quantum computation with Majorana zero modes Alan Tran, Alex Bocharov, Bela Bauer, Parsa Bonderson One of the main challenges for quantum computation is that while the number of gates required to perform a nontrivial computation may be very large, decoherence and errors in realistic architectures limits the number of physical gate operations that can be performed coherently. Therefore, an optimal mapping of the quantum algorithm into the physically available set of operations is of crucial importance. We examine this problem for a measurementonly topological quantum computer based on Majorana zero modes (MZMs), where gates are performed through sequences of measurements. Such a scheme has been proposed as a practical, scalable approach to process quantum information in an array of topological MZM qubits. Building on previous work that has shown that multiqubit Clifford gates can be enacted in a topologically protected fashion in such qubit networks, we discuss methods to obtain the optimal measurement sequence for a given Clifford gate under the constraints imposed by the physical architecture, such as layout and the relative difficulty of implementing different measurements. Our methods also provide tools for comparative analysis of different architectures and strategies, given experimental characterizations of particular aspects of the systems under consideration. 
Monday, March 2, 2020 9:48AM  10:00AM 
A07.00010: Computational universality of symmetryprotected topologically ordered cluster phases on 2D Archimedean lattices Austin Daniel, Rafael Alexander, Akimasa Miyake Which symmetryprotected topologically ordered (SPTO) ground states can be used for universal measurementbased quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global onsite symmetries but also by subsystem symmetries, which are finegrained symmetries dependent on the lattice geometry. Recently, all states within socalled SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetry and associated structures of quantum cellular automata. Motivated by this, we analyze the computational capability of SPTO cluster phases on all vertextranslative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1form symmetries, and the former three are fundamentally in onetoone correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1form symmetry and have a different capability related to error correction. 
Monday, March 2, 2020 10:00AM  10:12AM 
A07.00011: Parafermions and Z_{3 }ChargeFlux attachment Peng Rao, Vijay Shenoy, Inti Sodemann A recent construction (Ann. Phys. 393, 234 (2018)) has introduced an interesting route to bosonization of fermions in two spatial dimensions by implementing a precise lattice version of fluxcharge binding. The idea is to modify Kitaev's Toric code so that the electric charge (e) and magnetic flux (m) are always created in a tight ``dipolar" pair ε (=e x m) which is a fermion, providing a way to represent any local fermionic Hamiltonian as a local Hamiltonian of spins. We discuss an extension of these ideas to the case of a Z_{N }toric which allows a bosonization of anyons with more general statitistical angles. We have focused particularly in the case of N=3. We wil prove that ground states in the torus in this case are at least threefold degenerate, and, discuss a model featuring a topological phase transition between a 3fold degenerate state and a 9fold degenerate ground state featuring parafermionic excitations. 
Monday, March 2, 2020 10:12AM  10:48AM 
A07.00012: Fun with fractons Invited Speaker: Dominic Williamson Interest in fracton topological order has grown explosively over the past several years, leading to a plethora of models that exhibit exotic topological physics tied to mobility constrained superselection sectors. At the same time a classification of even the simplest class of stabilizer fracton Hamiltonians remains elusive. I will describe some recent efforts to tame the vast array of models with the goal of a systematic construction and classification of all topological phases of matter in three spatial dimensions. 
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