Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quantum groups”

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 145 records · Page 8

Analyzing the Free States of one Quantum Resource Theory as Resource States of Another

In the context of quantum resource theories (QRTs), free states are defined as those that can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. Here, in this work, we contribute to this body of knowledge by analyzing the resourcefulness in free states for—and across witnesses of—the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance, and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Universal fine grained asymptotics of free and weakly coupled quantum field theory

We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρ α (E) for each irreducible representation α of G obeys a universal formula as conjectured by Harlow and Ooguri. We further prove that this continues to hold in a weakly coupled quantum field theory, given an appropriate scaling of the coupling with temperature. This generalizes similar results that were previously obtained in (1 + 1)-D to higher spacetime dimension. We discuss the role of averaging in the density of states, and we compare and contrast with the case of continuous group G, where we prove a universal, albeit different, behavior.

Discrete Symmetries↗

Superconductivity in a topological lattice model with strong repulsion

The highly tunable nature of synthetic quantum materials-both in the solid-state and cold atom contexts-invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce the "double Hofstadter"model, a minimal 2D lattice model that incorporates exactly these features: Time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. Further, at the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the quantum spin Hall insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be p-wave-reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Consistent thermodynamic properties for alicyclic components of jet fuels: Experimental data, estimation methods, and homologous series trends

Alkylcycloalkanes represent a significant fraction of jet fuel components. An evaluation of their thermodynamic properties, enthalpies of formation in liquid and gas phases and enthalpies of vaporization, was conducted. A combination of available experimental data, up-to-date group-contribution methods, high-level quantum-chemical calculations, and homologous series trends was used to identify outliers and to recommend the most reliable values. The group-contribution approach was found to work well for the enthalpies of vaporization. Its performance for the enthalpies of formation in the liquid and gas phases was found to be substantially less effective, especially considering notable differences in this property among stereoisomers. Computationally affordable high-level ab initio results and homologous series trend analysis appeared more reliable. In conclusion, the recommended property values for 212 individual compounds and their isomeric mixtures were provided.

09 BIOMASS FUELS↗

Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms—even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Extracting Higher Central Charge from a Single Wave Function

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_ is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_ to gapping out the edge. Here, in this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1) 2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spin dynamics of the generalized quantum spin compass chain

Here we calculate the dynamical spin structure factor of the generalized spin-1/2 compass spin chain using the density matrix renormalization group. The model, also known as the twisted Kitaev spin chain, was recently proposed to be relevant for the description of the spin chain compound CoNb 2 O 6 . It features bond-dependent interactions and interpolates between an Ising chain and a one-dimensional variant of Kitaev's honeycomb spin model. The structure factor, in turn, is found to interpolate from gapped and nondispersive in the Ising limit to gapless with nontrivial continua in the Kitaev limit. In particular, the component of the structure factor perpendicular to the Ising directions changes abruptly at the Kitaev point into a dispersionless continuum due to the emergence of an extensive ground-state degeneracy. We show this continuum is consistent with analytical Jordan-Wigner results. We also discuss implications for future inelastic scattering experiments and applications to materials, particularly CoNb 2 O 6 .

1-dimensional spin chains↗

Triple Emission of 5'-( para -R-Phenylene)vinylene-2-(2'-hydroxyphenyl)benzoxazole (PVHBO). Part I: Dual Emission from the Neutral Species

The effects of 5'-(para-R-phenylene)vinylene (PV) substituents on the emission properties of 2-(2'-hydroxyphenyl)benzoxazole (HBO) are analyzed using steady-state and time-resolved absorption and emission spectroscopies in addition to quantum chemical calculations. All members in the series of PVHBOs are capable of excited-state intramolecular proton transfer (ESIPT) with a solvent sensitivity that is typical of a HBO derivative to produce a normal (aka enol) emission and an excited-state tautomer (aka keto) emission. These two emission bands of the neutral dyes are discussed in the current paper. The intermolecular proton transfer, i.e., the deprotonation, of a PVHBO results in the third band of the triple emission, which is described in the succeeding paper. The placement of an electron-withdrawing substituent R on the PVHBO scaffold increases the intensity of the keto emission relative to the enol emission in hydrogen-bonding solvents. The R substituents do not significantly alter the wavelengths of the enol and keto emission bands, which are located in the blue and green regions, respectively, of the visible spectrum. The ultrafast time-resolved spectroscopies and quantum chemical calculations offer explanations on how the R group and the solvent affect the enol and keto emission properties (i.e., wavelength, lifetime, fluorescence quantum yield, and relative ratio of their emissions). Here, the key findings include the following: (1) the emission energies of both enol and keto forms are not sensitively dependent on the R substituent and (2) the solvent-engaged enol excited state is quenched more efficiently as the R substituent becomes more electron-withdrawing. A PVHBO acts as a fusion of HBO and stilbenoid that intersect at the hydroxyphenyl moiety. Depending on the solvent and other environmental conditions, PVHBOs may exhibit the ESIPT property of HBO or the substituent-dependent emission of stilbenoid. This paper and the succeeding article provide a photophysical model of PVHBOs to explain the wavelengths and relative abundances of the three emission bands (enol, keto, and anion) that these compounds are able to produce. Judicial selection of the environmental factors may drive the emission of a PVHBO into the spectral regions of blue, green, and, in a couple of cases, orange or red.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A universal formula for the density of states in theories with finite-group symmetry

In this study we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero density, this gives a new proof of the completeness hypothesis for finite gauge fields. Inspired by the generality of the argument we further propose that the formula applies at high energy in any quantum field theory with a finite-group global symmetry, and give some evidence for this conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Primitive quantum gates for an S U ( 3 ) discrete subgroup: Σ ( 36 × 3 )

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ ( 36 × 3 ) group. This is the first time a non-Abelian crystal-like subgroup of S U ( 3 ) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ ( 36 × 3 ) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

Anand, Namit [NASA, Ames; Unlisted, US] (ORCID:000↗

Order-disorder in room-temperature ionic liquids probed via methyl quantum tunneling

Room-temperature ionic liquids are promising candidates for applications ranging from electrolytes for energy storage devices to lubricants for food and cellulose processing to compounds for pharmaceutics, biotransformation, and biopreservation. Due to the ion complexity, many room-temperature ionic liquids readily form amorphous phases upon cooling, even at modest rates. Here, we investigate two commonly studied imidazolium-based room-temperature ionic liquids, 1-ethyl-3-methylimidazolium tetrafluoroborate and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, as well as their mixtures, to demonstrate how the complex interplay between the crystalline and amorphous phases is affected by the processing conditions, such as thermal history, liquid mixing, and applied pressure. We show that quantum tunneling in the cation methyl groups, measured by high-resolution inelastic neutron scattering, can be used to probe the order-disorder in room-temperature ionic liquids (crystalline vs amorphous state) that develops as a result of variable processing conditions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantum for Energy Systems and Technologies

Quantum Information Science (QIS) is expected to profoundly change the practice of science and engineering in the coming decades. QIS technology exploits quantum phenomena for performing tasks that are impossible to do today and is a rapidly progressing field, fueled by large investments from the private sector and governments. Its importance to the U.S. economy and national security is underscored by the National Quantum Initiative Act (NQIA) passed in December 2018, which creates a coordinated multiagency program to support research and training in QIS. After the NIQA signed into law, NETL has launched an initiative to apply QIS to problems encountered in energy technology development. In Jan. 2020, an Quantum for Energy Systems & Technologies (QUEST) working group was formed to establish a workforce capable of developing, reviewing, managing, and advising on QIS-related technologies for NETL and FECM. Since then, the QUEST team have been working on developing quantum sensing technology and performing quantum computing to solve energy-related problems. This poster summarized the QUEST team’s activities & accomplishments on QIS targeting energy-related applications.

Paudel, Hari P.↗

Mass gaps of a Z 3 gauge theory with three fermion flavors in 1 + 1 dimensions

We consider a Z 3 gauge theory coupled to three degenerate massive flavors of fermions, which we term Quantum Z(3) Dynamics, QZD. The spectrum can be computed in 1 + 1 dimensions using tensor networks. In weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial, analogous to those of nonrelativistic QED in 1 + 1 dimensions. In strong coupling, besides the usual baryon, the singlet meson is a baryon-antibaryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Information-theoretic aspects of Werner states

Highlights: • The rich structures of Werner states are reviewed. • Werner states are characterized in terms of quantum uncertainty. • Information-theoretic aspects of Werner states are revealed. In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner–Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗