Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session A38: Topological Quantum Information: Topological Phases, ErrorCorrecting Codes, and EntanglementRecordings Available

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Sponsoring Units: DQI Chair: Carolyn Zhang, University of Chicago Room: McCormick Place W195 
Monday, March 14, 2022 8:00AM  8:12AM 
A38.00001: Hybrid Fracton Phases: Parent Orders for Liquid and NonLiquid Quantum Phases Wenjie Ji We introduce hybrid fracton orders: threedimensional gapped quantum phases that exhibit the phenomenology of both conventional threedimensional topological orders and fracton orders. Hybrid fracton orders host both (i) mobile topological quasiparticles and loop excitations, as well as (ii) pointlike topological excitations with restricted mobility, with nontrivial fusion rules and mutual braiding statistics between the two sets of excitations. We study the detailed properties of hybrid fracton phases through exactly solvable models in which the resulting orders hybridize a threedimensional Z2 topological order with (i) the XCube fracton order, or (ii) Haah's code. The hybrid orders presented here can also be understood as the deconfined phase of a gauge theory whose gauge group is given by an Abelian global symmetry G and subsystem symmetries of a normal subgroup N along lowerdimensional subregions. We further generalize the hybrid fracton orders to nonAbelian cases where G is a discrete nonAbelian finite group. The nonAbelian hybrid fracton orders host immobile, pointlike nonAbelian excitations. 
Monday, March 14, 2022 8:12AM  8:24AM 
A38.00002: Subsystem criticality & bifurcating entanglement renormalization Dominic J Williamson Gapped fracton topological phases satisfy the definition of topological quantum order and yet exhibit unconventional properties including bifurcation under entanglement renormalization transformations. A direction of current interest concerns gapless phase transition points that are related to fracton topological phases. Motivated by this, I will describe a bifurcating entanglement renomalization group flow that is based on the critical (1+1)D Ising model. I will go on to show that this defines a tensor network state with some unusual correlation function behavior. 
Monday, March 14, 2022 8:24AM  8:36AM 
A38.00003: Classification of NonUnitary MTC and Topological Phases Donghae Seo, Minyoung You, HeeCheol Kim, Gil Young Cho Unitary modular tensor categories (MTCs) can characterize 2+1D topological phases with their modular data. Due to the rankfiniteness for MTCs, there have been many efforts to classify MTCs by the rank. Recent studies classified MTCs (both unitary and nonunitary) completely up to rank 5, and partially for higher ranks. Meanwhile, modular data of nonunitary MTCs characterize nonunitary conformal field theories, which are relevant for the YangLee singularity or Gaffnian quantum Hall states. We classify nonunitary MTCs with rank greater than 5 computationally by checking consistency conditions of category theory and present the table of nonunitary MTCs for low ranks. Importantly, the consistency conditions for nonunitary MTCs can be obtained from that of unitary MTCs by allowing negative quantum dimensions, or equivalently allowing negative first row entries of the S matrices. Our classification table contains the fusion rules, the central charges, the quantum dimensions, and the modular data of each nonunitary MTC. We believe that our table would be a useful reference for researchers who study category theory or topological phases. 
Monday, March 14, 2022 8:36AM  8:48AM 
A38.00004: Irreducible multipartite correlations as an order parameter for klocal nontrivial states Ali Lavasani, Yahya Alavirad Geometrically nontrivial quantum states can be defined as states that cannot be prepared by a constant depth geometrically local unitary circuit starting from a product state. However, for topological phases, as well as a large class of quantum error correcting codes without an underlying geometric structure, the required circuit depth remains infinite even if we replace the condition of geometric locality with the weaker condition of klocality. Motivated by this observation, we look for a nongeometric quantity that can capture klocal nontriviality of a given state, for example, we ask if it is possible to distinguish the ground state of the toric code from a trivial state without having access to the position label of the qubits. We observe that a fundamental property of klocal nontrivial states is the presence of irreducible manypartite correlations shared between an infinitely large number of randomly chosen parties, i.e. correlations that cannot be inferred by accessing only a finite number of parties. We introduce an order parameter designed to capture such correlations. We demonstrate the utility of our order parameter by applying it to a wide variety of examples: The toric code on a square lattice, random stabilizer states, quantum expander codes, and a particular holographic stabilizer state. We discuss general relations between this order parameter and the erasure thresholds of quantum error correcting codes as well as the classical bond percolation problem. 
Monday, March 14, 2022 8:48AM  9:00AM 
A38.00005: Observation of SymmetryProtected Selection Rules in Periodically Driven Quantum Systems GUOQING WANG, Changhao Li, Paola Cappellaro Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Timeperiodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particlehole symmetries, by observing symmetryinduced Floquet selection rules. Notably, we exploit modulated driving to reach the strong lightmatter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogenvacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetryprotected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems. 
Monday, March 14, 2022 9:00AM  9:12AM 
A38.00006: A holographic view of topological stabilizer codes Nathanan Tantivasadakarn, Thomas Schuster, Ashvin Vishwanath, Norman Y Yao We study boundaries of topological stabilizer codes and the constraints imposed on them by the emergent conservation laws that govern the bulk topological order. We show at the level of the boundary operator algebra without referring to a particular boundary Hamiltonian that these constraints forbid the boundary from being realized via a local tensor product Hilbert space. Furthermore, we demonstrate that the different ways in which the boundary Hilbert space fails to be a tensor product directly encode topological properties of the bulk. In particular, we find quantities of the boundary operator algebra that are directly related to the self and mutual statistics of bulk excitations. We demonstrate this explicitly in a variety of topological stabilizer codes, including Type I and II fracton codes. 
Monday, March 14, 2022 9:12AM  9:24AM 
A38.00007: Pauli topological stabilizer codes from twisted quantum doubles Tyler D Ellison, YuAn Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, Dominic J Williamson We construct a Pauli stabilizer code for every twodimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer code, defined on fourdimensional qudits, belonging to the double semion (DS) phase of matter. We find an explicit finitedepth quantum circuit (with ancillary qubits) that maps the ground state subspace of the DS stabilizer code to that of the DS stringnet model. The DS stabilizer code is constructed by condensing an emergent boson in a Z_{4} toric code, which can be implemented by making certain twobody measurements. We show that the construction of the DS stabilizer code generalizes to all twisted quantum doubles with Abelian anyons, yielding models defined on compositedimensional qudits. Our work thus extends the classification of Pauli topological stabilizer codes beyond stacks of toric codes. We also demonstrate that certain symmetryprotected topological phases can be modeled by Pauli stabilizer codes by gauging 1form symmetries of the twisted quantum double stabilizer codes. 
Monday, March 14, 2022 9:24AM  9:36AM 
A38.00008: Entanglement cost in topological stabilizer models at finite temperature HungHwa Lin, TsungCheng Lu, EnJui Kuo The notion of entanglement has been useful for charactering quantum manybody systems. From the perspective of quantum information theory, it is tempting to ask whether their entanglement structures possess any operational meanings, e.g., measuring the cost of preparing an entangled system using only local operations and classical communication (LOCC). While the answer is affirmitive for pure states in that entanglement entropy coincides with entanglement cost, the case for mixedstates such as systems described by thermal Gibbs states is less understood. To this end, we address this question by studying a recently proposed quantity dubbed κentanglement, which not only measures entanglement for mixed states but also quantifies the entanglement cost under positivepartialtranspose (PPT) preserving operations. In particular, we focus on Gibbs states of ddimensional toric code models for d = 2, 3, 4, and show that their κentanglement coincides with entanglement negativity, which has been known to diagnose topological order at finite temperature. Our finding therefore provides an operational meaning for their longrange entanglement structure. 
Monday, March 14, 2022 9:36AM  9:48AM 
A38.00009: Chiral central charge from a single bulk wave function Bowen Shi, Isaac Kim, Kohtaro Kato, Victor V Albert A (2+1)dimensional gapped quantum manybody system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the manybody ground state wave function in the bulk. According to our formula, a nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being realvalued in any local product basis. 
Monday, March 14, 2022 9:48AM  10:00AM 
A38.00010: Multipartitioning topological phases by vertex states and quantum entanglement Yuhan Liu, Ramanjit Sohal, Jonah L KudlerFlam, Shinsei Ryu We discuss multipartitions of the gapped ground states of (2+1)dimensional topological liquids into three spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulkboundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)dimensional conformal field theory  these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states. This approach allows an explicit construction of the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a nontrivial distribution of the spectrum of the partially transposed density matrix. For reflected entropy, we test the recent claim that states the difference between reflected entropy and mutual information is given, once short range correlations are properly removed, by (c/3)\ln 2 where c is the central charge of the topological liquid that measure ungappable edge degrees of freedom. As specific examples, we consider topological chiral pwave superconductors and Chern insulators. 
Monday, March 14, 2022 10:00AM  10:12AM 
A38.00011: Topological graph states and quantum error correction codes Pengcheng Liao, David L Feder, Barry C Sanders Identifying and characterizing topological order is of widespread importance to both condensed matter physics and quantum information theory. In this work, we focus on the graphstate representation of stabilizer topological quantum error correction codes (QECCs). We derive a set of necessary and sufficient conditions for a family of graph states to be in TQO1, a class of QECC states whose code distance (i.e. the number of protected singlequbit errors) scales macroscopically with the number of physical qubits. Using these criteria, we consider a number of specific graph families and discuss which are topologically ordered and how to construct the codewords. This formalism is then employed to construct several QECCs with macroscopic distance, including a new threedimensional topological code generated by local stabilizers that also has a macroscopic number of encoded logical qubits. The results indicate that graph states provide a fruitful approach to the construction and characterization of topological stabilizer QECCs. 
Monday, March 14, 2022 10:12AM  10:24AM 
A38.00012: Understanding entanglement negativity in topological order at finite temperature TsungCheng Lu, Sagar Vijay It has been proposed that the stability of topologically ordered states of matter at finite temperature can be diagnosed by their longrange entanglement structure using entanglement negativity, a mixedstate entanglement measure. In this work, we provide a novel connection between entanglement negativity in a topological order and an emergent symmetryprotected topological (SPT) order localized on the entanglement bipartition. This connection leads to a precise understanding of the phase transition in entanglement negativity as the temperature is increased, and as thermal fluctuations eventually destroy the longrange entanglement in the topological phase. Within this correspondence, anyons in topological order correspond to symmetry charges in SPT order, and the stability of topological order at a nonzero temperature relates to the stability of SPT order against a symmetrybreaking field. For the 4d toric code and 3d toric code with pointlike charges forbidden, in which topological order exists at finite temperature, the corresponding SPT order is protected by a higherform symmetry that is robust under a weak symmetrybreaking field. Finally, a universal scaling form of longrange entanglement negativity is derived across the finite temperature transition of topological order. 
Monday, March 14, 2022 10:24AM  10:36AM 
A38.00013: Optimal thresholds for fracton codes and random spin models with subsystem symmetry Hao Song, Janik SchönmeierKromer, Ke Liu, Oscar Viyuela, Lode C Pollet, Miguel Angel MartinDelgado We study optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the errorcorrection process for bitflip and phaseflip noises into novel statistical models with Ising variables and random multibody couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We use parallel tempering Monte Carlo simulations to obtain disordertemperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the Xcube fracton code displays a minimum error threshold that is much higher than 3D topological codes such as the toric code and the color code. This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms. 
Monday, March 14, 2022 10:36AM  10:48AM 
A38.00014: Topology of hole spins in semiconductor quantum dots Joseph E Zwiener, Sanjay Prabhakar In this talk, we discuss a method to flip the heavy hole spin of semiconductor quantum dots completely by an adiabatic transport of dots in the plane of twodimensional electron gas. We estimate the geometric spin flip time for heavy holes which turned out to be much shorter time than the experimentally reported decoherence time that may provide an alternative route to flip the topologically protected heavy hole spin before reaching decoherence. By utilizing Feynman disentangling operator scheme, we find evolution matrix of heavy hole and then discuss the influence of pure Rashba and Dresshaus spinorbit coupling effects on the geometric spinflip probabilities due to the adiabatic motion of dots in the 2D plane. Our study may be useful for building solidstate realization of quantum computing devices 
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