Search NASA⌕ Search

SEARCH · Search NASA

Results for “topological quantum computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Generalized Hall conductivities in local commuting projector models: Generalized symmetries and protected surface modes

Hall conductivities are important characterizations of phases of matter. It is known that nonzero Hall conductivities are difficult to realize in local commuting projector lattice models due to no-go theorems in (2+1)⁢D. In this work we construct local commuting projector models in (2+1)⁢D and (3+1)⁢D with nonzero generalized Hall conductivities for ordinary and higher-form continuous symmetries on tensor product Hilbert space of finite local dimension. The model is given by a standard ℤ 𝑁 toric code, but the symmetries do not admit expression in terms of on-site charge operators. The symmetry do not have local charges or currents on the lattice in the absence of boundaries, but there is still a notion of Hall conductivities that coincide with the continuum field theories. We construct protected gapless boundaries of the lattice models using modified Villain formalism. The generalized Hall conductivities are computed by surface currents as well as bulk flux insertion and many-body Chern number.

Anomalies↗
DOE OSTI2020

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms

We formulate a family of spin Topological Quantum Field Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf–Witten TQFTs. They are obtained by gauging G-equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a finite group G symmetry. We use the fact that the torsion part of the classification is given by Pontryagin duals to spin-bordism groups of the classifying space BG. We also consider unoriented analogues, that is G-equivariant invertible pin ± -TQFTs (fermionic time-reversal-SPTs) and their gauging. We compute these groups for various examples of abelian G using Adams spectral sequence and describe all corresponding TQFTs via certain bordism invariants in 3, 4 and other dimensions. This gives explicit formulas for the partition functions of spin-TQFTs on closed manifolds with possible extended operators inserted. The results also provide explicit classification of ’t Hooft anomalies of fermionic QFTs with finite abelian group symmetries in one dimension lower. We construct new anomalous boundary spin-TQFTs (surface fermionic topological orders). Finally, we explore SPT and symmetry enriched topologically (SET) ordered states, and crystalline SPTs protected by space-group (e.g. translation Z) or point-group (e.g. reflection, inversion or rotation C m ) symmetries, via the layer-stacking construction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On topological approach to local theory of surfaces in Calabi–Yau threefolds

In this work, we study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson- Thomas gauge theory and its reductions to D = 4 and D = 2 which are relevant to the local theory of surfaces in Calabi-Yau threefolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Computational Study of Field Initiated Surface Reactions for Synthesis of Diamond and Silicon

This project involves using quantum chemistry to simulate surface chemical reactions in the presence of an electric field for nanofabrication of diamond and silicon. A field delivered by a scanning tunneling microscope (STM) to a nanometer scale region of a surface affects chemical reaction potential energy surfaces (PES) to direct atomic scale surface modification to fabricate sub-nanometer structures. Our original hypothesis is that the applied voltage polarizes the charge distribution of the valence electrons and that these distorted molecular orbitals can be manipulated with the STM so as to change the relative stabilities of the electronic configurations over the reaction coordinates and thus the topology of the PES and reaction kinetics. Our objective is to investigate the effect of applied bias on surface reactions and the extent to which STM delivered fields can be used to direct surface chemical reactions on an atomic scale on diamond and silicon. To analyze the fundamentals of field induced chemistry and to investigate the application of this technique for the fabrication of nanostructures, we have employed methods capable of accurately describing molecular electronic structure. The methods we employ are density functional theory (DFT) quantum chemical (QC) methods. To determine the effect of applied bias on surface reactions we have calculated the QC PESs in various applied external fields for various reaction steps for depositing or etching diamond and silicon. We have chosen reactions which are thought to play a role in etching and the chemical vapor deposition growth of Si and diamond. The PESs of the elementary reaction steps involved are then calculated under the applied fields, which we vary in magnitude and configuration. We pay special attention to the change in the reaction barriers, and transition state locations, and search for low energy reaction channels which were inaccessible without the applied bias.

Musgrave, Charles Bruce↗
DOE OSTI2016

Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at m = 2 3 magnetization

In this work, we perform an exact-diagonalization study of the spin- 1 2 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m = 2 3 with an emphasis on the X Y point ( J z = 0 ) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90 , 174409 (2014) ] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σ x y = 1 2 . Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σ x y = 1 2 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Complex saddles and Euclidean wormholes in the Lorentzian path integral

We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms of a 3-form flux, which include the Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. We also analyze the stability of the Giddings-Strominger wormhole in the 3-form picture, where we find that it represents a perturbatively stable Euclidean saddle of the gravitational path integral. This calls into question the ultimate fate of such solutions in an ultraviolet-complete theory of quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Alternative algebraic approaches in quantum chemistry

Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Probing the geometry of the Laughlin state

It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantumHall states—the filling v = 1/3 Laughlin state.We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulk off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a ‘pair amplitude’ operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. Furthermore, these various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

3d modularity

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d N = 2 theories where such structures a priori are not manifest. These modular structures include: mock modular forms, SL(2,$\mathbb{Z}$) Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Invariance of Topological Indices Under Hilbert Space Truncation

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possible application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

PANNA: Properties from Artificial Neural Network Architectures

We report prediction of material properties from first principles is often a computationally expensive task. Recently, artificial neural networks and other machine learning approaches have been successfully employed to obtain accurate models at a low computational cost by leveraging existing example data. Here, we present a software package “Properties from Artificial Neural Network Architectures” (PANNA) that provides a comprehensive toolkit for creating neural network models for atomistic systems following the Behler–Parrinello topology. Besides the core routines for neural network training, it includes data parser, descriptor builder for Behler–Parrinello class of symmetry functions and force-field generator suitable for integration within molecular dynamics packages. PANNA offers a variety of activation and cost functions, regularization methods, as well as the possibility of using fully-connected networks with custom size for each atomic species. PANNA benefits from the optimization and hardware-flexibility of the underlying TensorFlow engine which allows it to be used on multiple CPU/GPU/TPU systems, making it possible to develop and optimize neural network models based on large datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Dynamic load balancing with enhanced shared-memory parallelism for particle-in-cell codes

Furthering our understanding of many of today’s interesting problems in plasma physics – including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects – requires large-scale kinetic simulations using particle-in-cell (PIC) codes. However, these simulations are extremely demanding, requiring that contemporary PIC codes be designed to efficiently use a new fleet of exascale computing architectures. To this end, the key issue of parallel load balance across computational nodes must be addressed. We discuss the implementation of dynamic load balancing by dividing the simulation space into many small, self-contained regions or ‘‘tiles,’’ along with shared-memory (e.g., OpenMP) parallelism both over many tiles and within single tiles. The load balancing algorithm can be used with three different topologies, including two space-filling curves. Here, we tested this implementation in the code Osiris and show low overhead and improved scalability with OpenMP thread number on simulations with both uniform load and severe load imbalance. Compared to other load-balancing techniques, our algorithm gives order-of-magnitude improvement in parallel scalability for simulations with severe load imbalance issues.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Physics↗
DOE OSTI2019

Digital memcomputing: From logic to dynamics to topology

Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear, point-dissipative dynamical systems engineered so that periodic orbits and chaos can be avoided. A given logic problem is first mapped into this type of dynamical system whose point attractors represent the solutions of the original problem. A DMM then finds the solution via a succession of elementary instantons whose role is to eliminate solitonic configurations of logical inconsistency (“logical defects”) from the circuit. By employing a supersymmetric theory of dynamics, a DMM can be described by a cohomological field theory that allows for computation of certain topological matrix elements on instantons that have the mathematical meaning of intersection numbers on instantons. We discuss the “dynamical” meaning of these matrix elements, and argue that the number of elementary instantons needed to reach the solution cannot exceed the number of state variables of DMMs, which in turn can only grow at most polynomially with the size of the problem. These results shed further light on the relation between logic, dynamics and topology in digital memcomputing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Floquet engineering of tilted and gapped Dirac bandstructure in 1T$$^\prime$$-MoS$$_2$$

Abstract We have developed a rigorous theoretical formalism for Floquet engineering, investigating, and subsequently tailoring most crucial electronic properties of 1T $$^\prime$$ ′ -MoS $$_2$$ 2 by applying an external high-frequency dressing field within the off-resonance regime. It was recently demonstrated that monolayer semiconducting 1T $$^\prime$$ ′ -MoS $$_2$$ 2 exhibits tunable and gapped spin- and valley-polarized tilted Dirac bands. The electron-photon dressed states depend strongly on the polarization of the applied irradiation and reflect a full complexity of the low-energy Hamiltonian for non-irradiated material. We have calculated and analyzed the properties of the electron dressed states corresponding to linear and circular polarization of a dressing field by focusing on their symmetry, anisotropy, tilting, direct and indirect band gaps. Circularly polarized dressing field is known for transition into a new electronic state with broken time-reversal symmetry and a non-zero Chern number, and therefore, the combination of these topologically non-trivial phases and transitions between them could reveal some truly unique and previously unknown phenomena and applications. We have also computed and discussed the density of states for various types of 1T $$^\prime$$ ′ -MoS $$_2$$ 2 materials and its modification in the presence of a dressing field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization in Co3Sn2S2

Abstract Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, based on the compelling identification of the two cleavable surfaces of Co 3 Sn 2 S 2 , we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co 3 Sn 2 S 2 surface. Such SKESs are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome-lattice network in the Co 3 Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co 3 Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome-lattice materials using conventional surface deposition techniques.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The concept of spin ice graphs and a field theory for their charges

Originally detected in rare earth pyrochlores, spin ice physics is now being artificially extended to a variety of geometries that control collective behavior and exotic properties, making graph theory their proper framework. We relate spin ice notions, such as ice rule, ice manifold, Coulomb phases, charges, and monopoles, to graph-theoretical notions, such as balance, in/out-degrees, and Euler paths. We then propose a field-theoretical treatment in which topological charges and monopoles are the degrees of freedom, while the binary spins are subsumed in an entropic interaction among charges. We show that for a spin ice on a graph in a Gaussian approximation, the kernel of the entropic interaction is the inverse of the graph Laplacian, and we compute screening functions from the graph spectra as Green operators for the screened Poisson problem on a graph. We then apply the treatment to star graphs, tournaments, cycles, and regular spin ice in different dimensions. Our aim is twofold: to set spin ice physics in a proper graph setting, where only topological rather than geometrical notions hold, and to invite graph theorists to contribute their powerful tools to the field of spin ice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum order by disorder in frustrated spin nanotubes

Here we investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a J1–J2 Heisenberg model at 45° around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a Z2 phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical η c = J 1 /2J 2 of the Z 2 -helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the Z 2 -helical phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗