We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c−. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (−1)F, specified by a second cohomology class [ω2]∈H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c−)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c−=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c− and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry.

1 aBarkeshli, Maissam1 aChen, Yu-An1 aHsin, Po-Shen1 aManjunath, Naren uhttps://arxiv.org/abs/2109.1103901492nas a2200181 4500008004100000245008600041210006900127260001500196490000600211520094800217100001601165700002301181700002101204700001701225700001701242700001401259856003701273 2022 eng d00aEfficient Product Formulas for Commutators and Applications to Quantum Simulation0 aEfficient Product Formulas for Commutators and Applications to Q c03/10/20220 v43 aWe construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

1 aChen, Yu-An1 aChilds, Andrew, M.1 aHafezi, Mohammad1 aJiang, Zhang1 aKim, Hwanmun1 aXu, Yijia uhttps://arxiv.org/abs/2111.1217702202nas a2200145 4500008004100000245009100041210006900132260001400201490000800215520174200223100001501965700001601980700002301996856003702019 2022 eng d00aEuler-obstructed Cooper pairing: Nodal superconductivity and hinge Majorana zero modes0 aEulerobstructed Cooper pairing Nodal superconductivity and hinge c3/29/20220 v1053 aSince the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where PT is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is time-reversal invariant and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models. Our work presents the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing.

1 aYu, Jiabin1 aChen, Yu-An1 aSarma, Sankar, Das uhttps://arxiv.org/abs/2109.0268501827nas a2200181 4500008004100000245005500041210005500096260001400151490000600165520130500171100002301476700001601499700001501515700002001530700003001550700002801580856003701608 2022 eng d00aPauli Stabilizer Models of Twisted Quantum Doubles0 aPauli Stabilizer Models of Twisted Quantum Doubles c3/30/20220 v33 aWe construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J. uhttps://arxiv.org/abs/2112.1139401306nas a2200121 4500008004100000245007000041210006900111260001500180520091800195100001601113700001801129856003701147 2021 eng d00aExactly Solvable Lattice Hamiltonians and Gravitational Anomalies0 aExactly Solvable Lattice Hamiltonians and Gravitational Anomalie c10/27/20213 aWe construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary Z2 topological order with fermionic particle and fermionic loop excitations that have mutual π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

1 aChen, Yu-An1 aHsin, Po-Shen uhttps://arxiv.org/abs/2110.1464401484nas a2200121 4500008004100000245010000041210006900141260001300210520107200223100001601295700001401311856003701325 2021 eng d00aHigher cup products on hypercubic lattices: application to lattice models of topological phases0 aHigher cup products on hypercubic lattices application to lattic c6/9/20213 aIn this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation in the simplicial case. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and deriving them from spacetime actions. In particular, we demonstrate explicitly that the (3+1)D SPT S=12∫w22+w41 (where w1 and w2 are the first and second Stiefel-Whitney classes) is dual to the 3-fermion Walker-Wang model constructed on the cubic lattice by Burnell-Chen-Fidkowski-Vishwanath. Other examples include the double-semion model, and also the `fermionic' toric code in arbitrary dimensions on hypercubic lattices. In addition, we extend previous constructions of exact boson-fermion dualities and the Gu-Wen Grassmann Integral to arbitrary dimensions. Another result which may be of independent interest is a derivation of a cochain-level action for the generalized double-semion model, reproducing a recently derived action on the cohomology level.

1 aChen, Yu-An1 aTata, Sri uhttps://arxiv.org/abs/2106.0527401816nas a2200169 4500008004100000245005500041210005500096260001500151520131100166100002301477700001601500700001501516700002001531700003001551700002801581856003701609 2021 eng d00aPauli stabilizer models of twisted quantum doubles0 aPauli stabilizer models of twisted quantum doubles c12/21/20213 aWe construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J. uhttps://arxiv.org/abs/2112.1139401689nas a2200145 4500008004100000245002500041210002500066260001400091520132300105100002101428700001601449700002001465700002101485856003701506 2020 eng d00aRaw Image Deblurring0 aRaw Image Deblurring c12/8/20203 aDeep learning-based blind image deblurring plays an essential role in solving image blur since all existing kernels are limited in modeling the real world blur. Thus far, researchers focus on powerful models to handle the deblurring problem and achieve decent results. For this work, in a new aspect, we discover the great opportunity for image enhancement (e.g., deblurring) directly from RAW images and investigate novel neural network structures benefiting RAW-based learning. However, to the best of our knowledge, there is no available RAW image deblurring dataset. Therefore, we built a new dataset containing both RAW images and processed sRGB images and design a new model to utilize the unique characteristics of RAW images. The proposed deblurring model, trained solely from RAW images, achieves the state-of-art performance and outweighs those trained on processed sRGB images. Furthermore, with fine-tuning, the proposed model, trained on our new dataset, can generalize to other sensors. Additionally, by a series of experiments, we demonstrate that existing deblurring models can also be improved by training on the RAW images in our new dataset. Ultimately, we show a new venue for further opportunities based on the devised novel raw-based deblurring method and the brand-new Deblur-RAW dataset.

1 aLiang, Chih-Hung1 aChen, Yu-An1 aLiu, Yueh-Cheng1 aHsu, Winston, H. uhttps://arxiv.org/abs/2012.04264