Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session B28: Topological Stabilization of Memory and ComputationFocus

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Sponsoring Units: DQI Chair: Torsten Karzig, Microsoft Room: BCEC 161 
Monday, March 4, 2019 11:15AM  11:27AM 
B28.00001: Spurious topological entanglement entropy and subsystem symmetries in compactified cubic code Dominic Williamson, Arpit Dua, Meng Cheng Compactifying one direction of the cubic code results in a family of two dimensional topological orders, equivalent to stacks of toric code enriched by translation symmetry. Surprisingly, some of these models have unbroken rigid 1D subsystem symmetries that lead to spurious contributions to the topological entanglement entropy. These spurious contributions can appear in a bulk computation of the topological entanglement entropy from a linear combination of subregion entropies with cancelling boundary terms. We introduce an entropic quantity that measures the presence of such spurious contributions. 
Monday, March 4, 2019 11:27AM  11:39AM 
B28.00002: Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes Seyed Ali Hosseini Lavasani, Maissam Barkeshli One of the most promising routes towards faulttolerant quantum computation utilizes topological quantum error correcting 
Monday, March 4, 2019 11:39AM  12:15PM 
B28.00003: Universal logical gate sets on encoded qubits using constant depth unitary circuits Invited Speaker: Maissam Barkeshli A basic question in the theory of faulttolerant quantum computation is to understand the fundamental spacetime overhead required for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. In this talk, I will demonstrate how braiding and Dehn twists in arbitrary (Abelian and nonAbelian) topological codes can be implemented through constant depth unitary circuits, where the depth is independent of the code distance. These circuits consist of a local constant depth unitary circuit followed by a permutation on physical qubits. When applied to the Fibonacci TuraevViro codes, they provide the first example of a universal logical gate set through constant depth unitary circuits. Other methods require either measurements, with followup gate operations that depend on the results of those measurements, or require local unitary circuits whose depth increases linearly with code distance. Our results can be extended to the context of hyperbolic TuraevViro codes as well, which have constant space overhead (constant rate encoding). I will discuss the faulttolerance properties of these circuits, and how they provide some of the most optimal schemes to date in terms of spacetime overhead for universal faulttolerant quantum computation. 
Monday, March 4, 2019 12:15PM  12:27PM 
B28.00004: Exotic quantum wires from symmetryenriched topological order interfaces Weiyi Ding, Shenghan Jiang, Jason Alicea When two identical chiral topological orders merge, the gapless modes at their interface can annihilate—thereby forming a single, uninterrupted topological phase. We study such interfaces when one of the two phases is promoted to a symmetryenriched topological order exhibiting an anyonpermuting symmetry. In this case symmetry provides an obstruction to gapping the interface; moreover, we show that the gapless, symmetrypreserving interface can realize nontrivial critical points with no finetuning required. Such exotic "quantum wires" can provide efficient building blocks for assembling twodimensional topological orders hosting anyons with universal braid statistics. 
Monday, March 4, 2019 12:27PM  12:39PM 
B28.00005: Reading the quantum state change of Majorana braiding ChunXiao Liu, ChingKai Chiu Braiding Majorana zero modes is an important approach to understand the physics of the nonAbelian statistics. To experimentally achieve this approach, accurately reading the change of the quantum state through the braiding process is an essential step. In this talk, we propose an experimental protocol to read the braiding change of the Majorana zero modes. The scheme includes four spatiallyseparated Majorana zero modes on top of a Coulomb blockaded topological superconductor. The reading of the braiding change is implemented by measuring the tunnel conductance in the strong Coulomb blockade regime for two overlapped Majorana zero modes. 
Monday, March 4, 2019 12:39PM  1:15PM 
B28.00006: Quantum ErrorCorrection for Fermionic Qubits Invited Speaker: Sagar Vijay Recently, there has been a growing effort to store quantum information in fermion states, so that a qubit is encoded in the fermion occupation number or the fermion number parity. Using fermions as the carriers of quantum information necessitates a new computational model and new errorcorrecting codes, as Fermi statistics forbids a mapping of local quantum gates acting on fermions to local gates acting on bosons. Motivated by ongoing experiments, we introduce a variety of fermionic quantum codes that are able to correct for fermion paritypreserving and parityviolating ("quasiparticle poisoning") errors. First, we discuss a surface code of Majorana fermions, along with its implementation, and demonstrate that the threshold errorrates for this code are superior to that of bosonic surface codes. We then introduce a generic construction of fermion codes from weakly selfdual classical, binary errorcorrecting codes, and use this method to find the shortest fermion code to correct for quasiparticle poisoning errors and other codes that correct higherweight errors. We conclude by discussing physical implementations of codes with shorter code distance. 
Monday, March 4, 2019 1:15PM  1:27PM 
B28.00007: Finitetemperature topological entanglement entropy for fractons Zhi Li, Roger Mong We consider the finitetemperature topological entanglement entropy (TEE) for topologicalordered systems. We found, quite generally, that the finitetemperature TEE is a piecewise constant function for CSS codes, which include the toric code and some fracton models like Haah's code and the Xcube model. We also discuss the phase transition structure of CSS codes and possible connections with selfcorrectness. 
Monday, March 4, 2019 1:27PM  1:39PM 
B28.00008: Scalable Fermionic Error Correction in 2D Majorana Surface Codes Oscar Viyuela, Sagar Vijay, Liang Fu The Majorana Surface Code (MSC) is a topological quantum code constructed out of interact 
Monday, March 4, 2019 1:39PM  1:51PM 
B28.00009: Categorizing Fracton Topological Order Arpit Dua, Dominic Williamson, Meng Cheng We employ quantities generalizing the twodimensional Smatrix invariant to categorize 3D stabilizers models into typeI fracton models, typeII fracton models, TQFTs and stacks of 2D Toric codes. These quantities count the numbers of anticommuting stringstring, stringmembrane and membranemembrane operators. The scaling behavior of these quantities with the size of the strings and membranes gives a signature of the class of topological order. We also investigate twodimensional compactifications of threedimensional fracton models. We find the twodimensional topological phases produced as a function of compactification radius and uncover translation symmetryenrichment that leads to twisted boundary conditions. This allows us to interpret the complicated ground space degeneracy of typeII 3D fracton models in terms of the symmetry enriched anyons in the compactified model. 
Monday, March 4, 2019 1:51PM  2:03PM 
B28.00010: Classifying Subsystem Symmetry Protected Topological Phases Trithep Devakul, Dominic Williamson, Yizhi You, Fiona Burnell, Shivaji Sondhi We discuss symmetry protected topological (SPT) phases in 2D systems with subsystem symmetries: symmetries which act on rigid subsystems, such as along straight lines or fractals. 
Monday, March 4, 2019 2:03PM  2:15PM 
B28.00011: A braiding quantum circuit based on the 4π Josephson effect John Stenger, Michael Hatridge, Sergey M Frolov, David Pekker We propose a topological qubit in which braiding and readout are mediated by the 4π MajoranaJosephson effect. The braidonium device consists of three Majorana nanowires that come together to make a trijunction; in order to control the superconducting phase differences at the trijunction the nanowires are enclosed in a ring made of a conventional superconductor; and in order to perform initialization/readout one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how fluxbased control and readout protocols can be used to demonstrate braiding and qubit operation for realistic materials and circuit parameters. 
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