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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗
DOE OSTI2025

Molecular axis distribution moments in ultrafast transient absorption spectroscopy: A path toward ultrafast quantum state tomography

In ultrafast time-resolved experiments with gas phase molecules, the alignment of the molecular axis relative to the polarization of the interacting laser pulses plays a crucial role in determining the dynamics following this light–matter interaction. The molecular axis distribution is influenced by the interacting pulses and is intrinsically linked to the electronic coherences of the excited molecules. However, in typical theoretical calculations of such interactions, the signal is either calculated for a single molecule in the molecular frame or averaged over all possible molecular orientations to compare with the experiment. Such averaging removes information about anisotropy in the molecular-axis distribution, even though anisotropic contributions can play a significant role in the measured experimental signal. Here, we calculate the laboratory frame transient electronic first-order polarization [P (1) ] spectra in terms of separated molecular frame and laboratory frame quantities. The laboratory frame polarizations are compared with orientation-averaged quantum master equation calculations, demonstrating that orientation-averaging captures only the isotropic contributions. We show that our formalism also allows us to evaluate the anisotropic contributions to the spectrum. Lastly, we discuss the application of this approach to achieve ultrafast quantum state tomography using transient absorption spectroscopy and field observables in nonlinear spectroscopy.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Paradigm for universal quantum information processing with integrated acousto-optic frequency beamsplitters

Frequency-bin encoding offers tremendous potential in quantum photonic information processing, in which a single waveguide can support hundreds of lightpaths in a naturally phase-stable fashion. This stability, however, comes at a cost: arbitrary unitary operations can be realized by cascaded electro-optic phase modulators and pulse shapers, but require nontrivial numerical optimization for design and have thus far been limited to discrete tabletop components. In this article, we propose, formalize, and computationally evaluate a new paradigm for universal frequency-bin quantum information processing using acousto-optic scattering processes between distinct transverse modes. We show that controllable phase matching in intermodal processes enables 2 × 2 frequency beamsplitters and transverse-mode-dependent phase shifters, which together comprise cascadable FRequency-transverse-mODe Operations (FRODOs) that can synthesize any unitary via analytical decomposition procedures. Modeling the performance of both random gates and discrete Fourier transforms, we demonstrate the feasibility of high-fidelity quantum operations with existing integrated photonics technology, highlighting prospects of parallelizable operations achieving 100% bandwidth utilization. Our approach is realizable with CMOS technology, opening the door to scalable on-chip quantum information processing in the frequency domain.

Lukens, Joseph M. [Purdue Univ., West Lafayette, I↗
DOE OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗
DOE OSTI2021

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Variational quantum eigensolver for approximate diagonalization of downfolded Hamiltonians using generalized unitary coupled cluster ansatz

In this paper we discuss the utilization of Variational Quantum Solver (VQE) and recently introduced Generalized Unitary Coupled Cluster (GUCC) formalism for the diagonalization of downfolded/effective Hamiltonians in active spaces. In addition to effective Hamiltonians defined by the downfolding of a subset of virtual orbitals we also consider their form defined by freezing core orbitals, which enables us to deal with larger systems. Furthermore, we also consider various solvers to identify solutions of the GUCC equations. We use N 2 , H 2 O, and C 2 H 4 , and benchmark systems to illustrate the performance of the combined framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Verified Optimizer for Quantum Circuits

We present VOQC, the first verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a small quantum intermediate representation, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. SQIR programs denote complex-valued matrices, as is standard in quantum computation, but we treat matrices symbolically to reason about programs that use an arbitrary number of quantum bits. SQIR’s careful design and our provided automation make it possible to write and verify a broad range of optimizations in VOQC, including full-circuit transformations from cutting-edge optimizers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Probing transverse momentum dependent structures with azimuthal dependence of energy correlators

We study the azimuthal angle dependence of the energy-energy correlators $\langle \mathcal{E}\left({\widehat{n}}_{1}\right)\mathcal{E}\left({\widehat{n}}_{2}\right)\rangle $ in the back-to-back region for e + e - annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers ${\mathbb{S}}_{i}$ in the back-to-back limit $\langle {\mathcal{E}}_{{\mathbb{S}}_{1}}\left({\widehat{n}}_{1}\right){\mathcal{E}}_{{\mathbb{S}}_{2}}\left({\widehat{n}}_{2}\right)\rangle $. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Photon-Instanton Collider Implemented by a Superconducting Circuit

Instantons, spacetime-localized quantum field tunneling events, are ubiquitous in correlated condensed matter and high-energy systems. However, their direct observation through collisions with conventional particles has not been considered possible. We show how recent advances in circuit quantum electrodynamics, specifically, the realization of galvanic coupling of a transmon qubit to a high-impedance transmission line, allows the observation of inelastic collisions of single microwave photons with instantons (phase slips). We develop a formalism for calculating the photon-instanton cross section, which should be useful in other quantum field theoretical contexts. In particular, we show that the inelastic scattering probability can significantly exceed the effect of conventional Josephson quartic anharmonicity and reach order-unity values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Perspective on Many-Body Methods for Molecular Polaritonic Systems

Recent advances in strong light–matter interactions have revealed a wealth of new physical phenomena in molecules embedded in optical cavities, including modified chemical reactivity, altered excitation spectra, and novel quantum correlations. To describe these effects from first-principles, the field of ab initio quantum electrodynamics (QED) has emerged as a compelling extension of quantum chemistry that treats electronic and photonic degrees of freedom on equal footing. In this Perspective, we review the growing landscape of many-body QED methods, including Hartree–Fock, density functional theory (QEDFT), time-dependent DFT (QED-TDDFT), configuration interaction (QED-CI), complete active space (QED-CASSCF), coupled cluster (QED-CC), quantum Monte Carlo (QED-QMC), and density matrix renormalization group (QED-DMRG), highlighting recent developments and implementations. We further explore real-time methods, gradient and Hessian formalisms, and the integration of nonadiabatic nuclear dynamics. Applications range from benchmark simulations of polaritonic chemistry to quantum simulations on emerging quantum hardware. We conclude by outlining future directions for theory development and interdisciplinary efforts at the interface of quantum chemistry, condensed matter, and quantum optics.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

Zylka, Christian↗
DOE OSTI2020

On the Virasoro six-point identity block and chaos

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Gauss Sum Strong Simulation v.0.1

Universal quantum circuits can be formulated in the Pauli measurement-based formalism as input T gate magic states, Clifford gates, and then multi-Pauli measurements. This code simulates single-Pauli measurements to show some theoretical bounds on the cost of full multi-Pauli measurements. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2020-14080 O

SciDAC↗
NASA NTRS1995

HZETRN: Description of a free-space ion and nucleon transport and shielding computer program

The high-charge-and energy (HZE) transport computer program HZETRN is developed to address the problems of free-space radiation transport and shielding. The HZETRN program is intended specifically for the design engineer who is interested in obtaining fast and accurate dosimetric information for the design and construction of space modules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmann transport equation with a straight-ahead approximation. The effect of the long-range Coulomb force and electron interaction is treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients with energies above a few A MeV are calculated by using Bethe's theory including Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear absorption cross sections are obtained from fits to quantum calculations and total cross sections are obtained with a Ramsauer formalism. Nuclear fragmentation cross sections are calculated with a semiempirical abrasion-ablation fragmentation model. The relation of the final computer code to the Boltzmann equation is discussed in the context of simplifying assumptions. A detailed description of the flow of the computer code, input requirements, sample output, and compatibility requirements for non-VAX platforms are provided.

Wilson, John W.↗
DOE OSTI2021

Generalized multifractality at spin quantum Hall transition

Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconductors of symmetry class C. Relations and differences with the conventional integer quantum Hall (IQH) transition are also studied. Using the field-theoretical formalism of non-linear sigma-model, we derive the pure-scaling operators representing generalizing multifractality and then “translate” them to the language of eigenstate observables. Performing numerical simulations on network models for SQH and IQH transitions, we confirm the analytical predictions for scaling observables and determine the corresponding exponents. Remarkably, the generalized-multifractality exponents at the SQH critical point strongly violate the generalized parabolicity of the spectrum, which implies violation of the local conformal invariance at this critical point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Entanglement Traffic Engineering in Quantum Optical Fiber Networks based on High-Dimensional Kerr Optical Frequency Combs

The purpose of the project was to explore the performance of entanglement protocols based on microresonator Kerr optical frequency combs. We have addressed these challenges by developing a rigorous frequency-bin approach that allowed us to determine an explicit steady-state density operator for quantum microcombs below threshold. Our novel approach has allowed us to derived an explicit formula for the density operator on the frequency-bin basis, and to propose a complete description of quantum Kerr combs regardless of the number of sidemodes or loss-induced coupling to the environment. This formalism also allows for the explicit determination of their fidelity, purity, and entropy. These results are expected to permit the exploitation of the full potential of entangled microcombs for quantum technology.

42 ENGINEERING↗
DOE OSTI2025

Nonperturbative quantum gravity in a closed Lorentzian universe

We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and real for each α-sector, as induced by spacetime wormholes. This appears to obstruct the conventional quantum-mechanical prescription of assigning probabilities via projection onto a basis of states. While previous approaches have introduced external observers or augmented the theory to resolve this issue, we argue that quantum gravity itself contains all the necessary ingredients to make physical predictions. We demonstrate that the emergence of classical observables and probabilistic outcomes can be understood as a consequence of partial observability: physical observers access only a subsystem of the universe. Tracing out the inaccessible degrees of freedom yields reduced density matrices that encode classical information, with uncertainties exponentially suppressed by the environment’s entropy. We develop this perspective using both the Lorentzian path integral and operator formalisms and support it with a simple microscopic model. Our results show that quantum gravity in a closed universe naturally gives rise to meaningful, robust predictions without recourse to external constructs.

AdS-CFT Correspondence↗
DOE OSTI2022

Possibilistic simulation of quantum circuits by classical circuits

In a breakthrough work, Bravyi, Gosset, and König (BGK) [Science 362, 308 (2018)] unconditionally proved that constant-depth quantum circuits are more powerful than their classical counterparts. Here, their result is equivalent to saying that a particular family of constant-depth quantum circuits takes classical circuits at least Ω⁡(log⁡n) depth to “simulate,” in a certain sense. In our paper, we formalize their sense of simulation, which we call “possibilistic simulation” or “p-simulation,” and construct explicit classical circuits that can p-simulate any depth-d quantum circuit with Clifford and t T-gates in depth O(d+t). Our classical circuits use {NOT,AND,OR} gates of fan-in ≤ 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗