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We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3 + 1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth quantum circuit (FDQC) that prepares the ground state from an unentangled symmetric state. The FDQC allows us to clearly demonstrate the characteristic properties of supercohomology phases -namely, symmetry fractionalization on fermion parity flux loops -predicted by continuum formulations. By composing the corresponding FDQCs, we also recover the stacking relations of supercohomology phases. Furthermore, we derive topologically ordered gapped boundaries for the supercohomology models by extending the protecting symmetries, analogous to the construction of topologically ordered boundaries for bosonic SPT phases. Our approach relies heavily on dualities that relate certain bosonic 2-group SPT phases with supercohomology SPT phases. We develop physical motivation for the dualities in terms of explicit lattice prescriptions for gauging a 1-form symmetry and for condensing emergent fermions. We also comment on generalizations to supercohomology phases in higher dimensions and to fermionic SPT phases outside of the supercohomology framework.

The production of fuels or chemicals from lignocellulose currently requires thermochemical pretreatment to release fermentable sugars. These harsh conditions also generate numerous small-molecule inhibitors of microbial growth and fermentation, limiting production. We applied small-insert functional metagenomic selections to discover genes that confer microbial tolerance to these inhibitors, identifying both individual genes and general biological processes associated with tolerance to multiple inhibitory compounds. Having screened over 248 Gb of DNA cloned from 16 diverse soil metagenomes, we describe gain-of-function tolerance against acid, alcohol, and aldehyde inhibitors derived from hemicellulose and lignin, demonstrating that uncultured soil microbial communities hold tremendous genetic potential to address the toxicity of pretreated lignocellulose. We recovered genes previously known to confer tolerance to lignocellulosic inhibitors as well as novel genes that confer tolerance via unknown functions. For instance, we implicated galactose metabolism in overcoming the toxicity of lignin monomers and identified a decarboxylase that confers tolerance to ferulic acid; this enzyme has been shown to catalyze the production of 4-vinyl guaiacol, a valuable precursor to vanillin production. These metagenomic tolerance genes can enable the flexible design of hardy microbial catalysts, customized to withstand inhibitors abundant in specific bioprocessing applications. Many lignocellulosic feedstocks (e.g., switchgrass) are preferred to maize, sugarcane, and other traditional food crops for the production of fuels and chemicals because they are able to grow on marginal land, often require little attention or energy input, and do not compete directly with the food supply (1-6). However, lignocellulose requires harsh thermochemical pretreatment methods to liberate fermentable monosaccharides (7-9), producing an additional compendium of compounds inhibitory to microbial growth that ultimately reduce production efficiencies (10-12). These small-molecule inhibitors derived from lignocellulose pretreatment (here called lignocellulosic inhibitors) are typically aldehydes, organic acids, furans, or phenolics and can originate from the cellulosic, hemicellulosic, and lignified fractions of the feedstock (11-15).Engineering hardier microbial production hosts with elevated tolerance to these inhibitors offers potential to ameliorate the toxic effects of these compounds without incurring the high process costs associated with detoxifying the lignocellulosic hydrolysate (16, 17). Unfortunately, the modes of toxicity of many of these toxins are poorly described, and genes conferring tolerance to many of these compounds have not been identified (18,19). An expanded catalog of tolerance-conferring genotypes may shed light on mechanisms of toxicity and enable synthetic biology approaches for the design of diverse production hosts with broadspectrum tolerance.Soil microorganisms, including white-rot fungi (20) and many bacteria (21), ar...

We construct fixed point lattice models for group supercohomology symmetry-protected topological phases of fermions ð2 þ 1ÞD. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build the ground states from a tensor product state. We then recover the classification of fermionic symmetry-protected topological phases, including the group structure under stacking, from the algebraic composition rules of these circuits. Furthermore, we show that the circuits are symmetric, implying that the group supercohomology phases can be many-body localized. Our strategy involves first building an auxiliary bosonic model, and then fermionizing it using the duality of Chen, Kapustin, and Radicevic. One benefit of this approach is that it clearly disentangles the role of the algebraic group supercohomology data, which are used to build the auxiliary bosonic model, from that of the spin structure, which is combinatorially encoded in the lattice and enters only in the fermionization step. In particular this allows us to study our models on 2D spatial manifolds of any topology, and to define a lattice-level procedure for ungauging fermion parity.

We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2×Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

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We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for bosonization at the level of quantum states. Thus, we use the TNO to provide an explicit algorithm for bosonizing fermionic projected entangled pair states (fPEPs). A key step in the algorithm is to account for a choice of spin-structure, encoded in a set of bonds of the bosonized fPEPS. This enables our tensor network approach to bosonization to be applied to systems on arbitrary triangulations of orientable 2D manifolds. CONTENTS

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e., not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U (1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2 n -dimensional qudits that feature surface anyons described by U (1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.