Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session Y29: Topological Quantum InformationFocus Live

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Sponsoring Units: DQI Chair: Roger Mong, University of Pittsburgh 
Friday, March 19, 2021 11:30AM  12:06PM Live 
Y29.00001: Quantum Error Correction: How To Get Below Threshold Invited Speaker: Barbara Terhal We review some novel developments in the theory of quantum error correction and discuss whether they could be useful for engineering quantum error correction in practice. We discuss some challenges in the realization of quantum error correction with superconducting transmon qubits such as qubit leakage and crosstalk. 
Friday, March 19, 2021 12:06PM  12:18PM Live 
Y29.00002: Experimental characterization of the 4D tensor monopole and topological nodal rings Changhao Li, Mo Chen, Giandomenico Palumbo, YanQing Zhu, Nathan Goldman, Paola Cappellaro Quantum mechanics predicts the existence of the Dirac and the Yang monopoles. Although their direct experimental observation in highenergy physics is still lacking, these monopoles, together with their associated vector gauge fields, have been demonstrated in synthetic matter. On the other hand, monopoles in evendimensional spaces have proven more elusive. A potential unifying framework–string theory–that encompasses quantum mechanics promotes the vector gauge fields to tensor gauge fields, and predicts the existence of more exotic tensor monopole in 4D space. Here we report the first experimental observation of a tensor monopole in a 4D parameter space synthesized by the spin degrees of freedom of a single solidstate defect in diamond. Using two complementary methods, we reveal the existence of the tensor monopole through measurements of its quantized topological invariant. By introducing a fictitious external field that breaks chiral symmetry, we further observe a novel phase transition to a topological nodal ring semimetal phase that is protected by mirror symmetries. 
Friday, March 19, 2021 12:18PM  12:30PM Live 
Y29.00003: Quantum circuits for topological state generation Pengcheng Liao, David L Feder Given their potential for faulttolerant operations, topological quantum states are currently the focus of intense activity. Topological states are generally obtained as the gapped degenerate ground states of a suitably chosen Hamiltonian. In the quantum circuit model of quantum state generation, however, one doesn't usually have access to the Hamiltonian. Interesting open questions include: what are the main properties that these states need to satisfy to ensure that they are topologically ordered, how can one prepare such a family of states on a quantum circuit, and what is the circuit complexity for the topological state preparation? In this work, we use the correspondence between stabilizer topological codes and graph states to obtain explicit families of quantum circuits for topological state generation. Making use of the relationship between topological order and quantum error correction codes with a code distance that scales as a polynomial in the number of qubits, we show that the scaling of quantum circuit depth complexity as the square root of the number of qubits when only geometrically local gates are permitted reduces to a logarithmic scaling if this restriction is relaxed. 
Friday, March 19, 2021 12:30PM  12:42PM Live 
Y29.00004: Protected superconducting qubit encoded in the topological phase of the transverse Ising model Clauderic OuelletPlamondon, Chloe Archambault, Razieh Annabestani, Gabriel EthierMajcher, Alireza NajafiYazdi The 1D transverse field Ising model (TFIM) is a wellstudied spin model which exhibits a topological phase transition when the coupling energy overcomes the onsite energy. Experimentally reaching the topological regime with atomic or photonic systems is challenging due to the prohibitively large coupling strength required. In this work, we present a superconducting circuit that can implement the topological phase of the TFIM. The circuit is composed of a chain of inductively coupled transmon qubits whose coupling strength and onsite energy can be tuned by biasing the couplers with an external flux. We show how the quasidegenerate ground states of the chain can be used to encode a logical qubit which is exponentially protected against charge noise. We estimate T1 as a function of the qubit coupling strength accounting for both ohmic and 1/f charge and flux noise. When the protection of the chain against charge noise is such that the flux noise becomes the dominant relaxation channel, we find an optimal T1 in the millisecond range. 
Friday, March 19, 2021 12:42PM  12:54PM Live 
Y29.00005: Z2 Lattice Gauge Theories and Kitaev’s Toric Code: A Scheme for Analog Quantum Simulation Lukas Homeier, Christian Schweizer, Arkady Fedorov, Fabian Grusdt Kitaev’s toric code is an exactly solvable model with Z2topological order, which has potential applications in quantum computation and error correction. Direct experimental realization remains an open challenge. Here we propose a building block for Z2 lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toriccode groundstate and its topological excitations. The proposed building block is realized in the secondorder coupling regime and is wellsuited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically nontrivial initial states during which a large gap on the order of the underlying coupling strength is present.This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the groundstate wavefunction and introduce a minimal braiding protocol. Detecting a \piphase shift between Ramsey fringes in this protocol reveals the anyonic excitations ofthe toriccode Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing nonAbelian anyons in analog quantum simulators. 
Friday, March 19, 2021 12:54PM  1:06PM Live 
Y29.00006: Persistence of Topological Phases in NonHermitian Quantum Walks Vikash Mittal, Aswathy Raj, Sanjib Dey, Sandeep Kumar Goyal Discretetime quantum walks are known to exhibit exotic topological states and phases. The physical realization of quantum walks in a noisy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the nonHermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in onedimensional splitstep quantum walk persists as long as the Hamiltonian is PTsymmetric. Although the topological nature persists in twodimensional quantum walks as well, the PTsymmetry has no role to play there. Furthermore, we observe the noiseinduced topological phase transition in twodimensional quantum walks. 
Friday, March 19, 2021 1:06PM  1:18PM Live 
Y29.00007: Measurementbased quantum gate teleportation and the degeneracy of the entanglement spectrum: beyond symmetry protected topological order Zhuohao Liu, David L Feder Quantum states with symmetry protected topological order (SPTO), such as the gapped degenerate ground states of the AKLT spin chain for a suitable choice of parameters, have a key common attribute: the Schmidt coefficients for the decomposition of any bipartite density operator are degenerate. This attribute is also shared by cluster states, the first resource to be identified for measurementbased quantum computation (MBQC), which obeys a global onsite symmetry. While the existence of SPTO is sufficient to ensure (noisy) MBQC, it is not clear what role the degeneracy of the entanglement spectrum itself plays; in principle it is possible that accidental degeneracy could suffice for MBQC, even in the absence of SPTO. We explore the implications of this possibility for quantum gate teleportation in onedimensional spin chains; while the teleported gates are offered no protection from errors in this scheme, it would greatly expand the resource states able to support MBQC. 
Friday, March 19, 2021 1:18PM  1:30PM Live 
Y29.00008: Symmetryprotected Sign Problem and Magic in Quantum Phases of Matter Tyler Ellison, Kohtaro Kato, ZiWen Liu, Timothy Hsieh We introduce the concepts of a symmetryprotected sign problem and symmetryprotected magic, defined by the inability of symmetric finitedepth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetryprotected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, onedimensional Z_{2} × Z_{2} SPT states (e.g. cluster state) have a symmetryprotected sign problem, and twodimensional Z_{2} SPT states (e.g. LevinGu state) have both a symmetryprotected sign problem and magic. We also comment on the relation of a symmetryprotected sign problem to the computational wire property of onedimensional SPT states and the greater implications of our results for measurement based quantum computing. 
Friday, March 19, 2021 1:30PM  1:42PM Live 
Y29.00009: Axionic Quantum Memory Noah BrayAli We propose to store quantum information in the form of a darkstate axionic polariton. The axion is a leading dark matter candidate which couples linearly to light in the presence of a background electromagnetic field. In symmetryprotected topological phases of matter, such as topological insulators and Weyl semimetals, axionlike modes arise when the symmetry that protects the phase spontaneously breaks down and an axion insulator phase is realized. By coherently controlling the background electromagnetic field, single photons can be converted into and retrieved from amplitude (phase) fluctuations of the spin (charge) density wave in topological insulators (Weyl semimetals). We study the feasibility of the proposal in the context of recent progress realizing and characterizing axion insulator phases in rareearth doped topological insulators and quasione dimensional Weyl semimetals. 
Friday, March 19, 2021 1:42PM  1:54PM Live 
Y29.00010: Topological quantum state transfer in the Creutz ladder Juan Zurita, Charles Creffield, Gloria Platero The Creutz ladder has recently attracted a great deal of attention. It is a quasi1D model threaded by a magnetic flux which can present nontrivial topology and AharonovBohm caging. The latter effect is caused by destructive interference and flattens the bands of the system, localizing the particles, bosonic or fermionic, in a small spatial region or cage. This model has been recently implemented experimentally [1,2]. The addition of Hubbard interactions, which can give rise to repulsively bound pairs termed doublons, has also been studied [3]. 
Friday, March 19, 2021 1:54PM  2:06PM Live 
Y29.00011: Quantum computational advantage with string order parameters of 1D symmetryprotected topological order Austin Daniel, Akimasa Miyake Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between small computational complexity classes of shallowdepth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of onedimensional symmetryprotected topological orders (SPTO), when an invariant of SPTO known as a twist phase is nontrivial and 1. Our construction demonstrates that general 1D SPTO with sufficiently large string order parameters possess globally constrained correlations useful for the unconditional computational separation. 
Friday, March 19, 2021 2:06PM  2:18PM Live 
Y29.00012: Robustness of topology of wavefunctions in NISQ quantum machines Xiao Xiao, James Freericks, Alexander F Kemper Evaluating topological invariants is an important way to characterize different topological quantum phases, which form a critical component in investigating quantum materials. Topological invariants are quantities that characterize the global geometrical properties of wave functions and thus are immune to local noise. Here we demonstrate a general way to measure the topological invariants on NISQ quantum computers. Due to their robustness, the topological invariants can be precisely obtained even in the presence of local noise, and in certain cases is even noisefree. We apply this approach on IBM quantum computers to a topological superconducting model, and show that strikingly the Chern number can be measured exactly without any error. Other topological invariants are not as robust as the Chern number measurement but can still qualitatively distinguish different topological phases. 
Friday, March 19, 2021 2:18PM  2:30PM On Demand 
Y29.00013: Observation of nonHermitian topology with nonunitary dynamics of solidstate spins Wengang Zhang, Xiaolong Ouyang, Xianzhi Huang, Xin Wang, huili zhang, yefei yu, Xiuying Chang, Dongling Deng, Luming Duan NonHermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulkboundary correspondence. Recently, they have attracted tremendous attentions and experimental observations of the nonHermitian skin effect have been reported in mechanical metamaterials, nonreciprocal topolectric circuits, and photonic systems. Here, we implement the nonHermitian SuSchriefferHeeger (SSH) hamiltonian, which is a prototypical model for studying nonHermitian topological phases, with a solidstate quantum simulator consisting of an electron spin and a 13C nuclear spin in a nitrogenvacancy center in a diamond. By employing a dilation method, we realize the desired nonunitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. Our result paves the way for further exploiting and understanding the intriguing properties of nonHermitian topological phases with solidstate spins or other quantum simulation platforms. 
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