Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “quantum probability”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Classical symmetries and the Quantum Approximate Optimization Algorithm

Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Many-Body Majorana Braiding without an Exponential Hilbert Space

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. Here, we show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.

Majorana bound states↗
DOE OSTI2023

Observation of half-integer Shapiro steps in graphene Josephson junctions

We study quantum transport and AC Josephson effect of hexagonal boron nitride encapsulated graphene (BGB) Josephson junctions (JJs). Our experiments reveal the emergence of the half-integer Shapiro steps in the n-type regime with high electron carrier densities. We attribute this observation to the gate-tunable transmission probability of the graphene junction. Furthermore, our numerical simulations are consistent with the appearance of half-integer Shapiro steps at high transparency, which suggests a skewed current phase relationship in the graphene JJ.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Reaching 90% Photoluminescence Quantum Yield in One-Dimensional Metal Halide C 4 N 2 H 14 PbBr 4 by Pressure-Suppressed Nonradiative Loss

Low-dimensional perovskite-related metal halides have emerged as a new class of light-emitting materials with tunable broadband emission from self-trapped excitons (STEs). Although various types of low-dimensional structures have been developed, fundamental understating of the structure–property relationships for this class of materials is still very limited, and further improvement of their optical properties remains greatly important. Here, we report a significant pressure-induced photoluminescence (PL) enhancement in a one-dimensional hybrid metal halide C 4 N 2 H 14 PbBr 4 , and the underlying mechanisms are investigated using in situ experimental characterization and first-principles calculations. Under a gigapascal pressure scale, the PL quantum yields (PLQYs) were quantitatively determined to show a dramatic increase from the initial value of 20% at ambient conditions to over 90% at 2.8 GPa. With in situ characterization of photophysical properties and theoretical analysis, we found that the PLQY enhancement was mainly attributed to the greatly suppressed nonradiative decay. Pressure can effectively tune the energy level of self-trapped states and increase the exciton binding energy, which leads to a larger Stokes shift. The resulting highly localized excitons with stronger binding reduce the probability for carrier scattering, to result in the significantly suppressed nonradiative decay. Overall, our findings clearly show that the characteristics of STEs in low-dimensional metal halides can be well-tuned by external pressure, and enhanced optical properties can be achieved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Scaling quantum approximate optimization on near-term hardware

The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Ground-state properties of the Hubbard model in one and two dimensions from the Gutzwiller conjugate gradient minimization theory

We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly adopted Gutzwiller approximation (GA), which is a major source of inaccuracy. Instead, the theory uses an approximation that is based on the occupation probability of the on-site configurations, rather than approximations that decouple the site-site correlations as used in the GA. We test the theory in the one-dimensional and two-dimensional Hubbard models at various electron densities and find that GCGM reproduces energies and double occupancies in reasonable agreement with benchmark data at a very small computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Universal relation between doping content and normal-state resistance in gate voltage tuned ultrathin Bi 2 Sr 2 CaCu 2 O 8 + x flakes

We report gate voltage tunable ultra-thin high-T c cuprates supply a unique platform to investigate the electronic phase diagram and superconductor-insulator transition. One of the challenges in this field is the precise determination of the doping content in the underdoped non-superconducting region. Here we report the discovery of a universal relation between the doping content p and the normal-state resistance at a fixed temperature R(T f ), p = α + β ln[1/R(T f )], in the ultra-thin Bi 2 Sr 2 CaCu 2 O 8+x flakes. The in-depth analysis shows that the evolution of carrier scattering probability with doping content and the change of effective mass caused by superconductor-insulator transition are two key factors leading to this logarithmic relation. Based on our finding, the more precise electronic phase diagram can be established. In addition, the superconductor-insulator transition is verified to be a quantum phase transition using a finite size scaling analysis. The scaling exponent z v is found to have a close correlation with the disorder levels. The present result provides an important foundation to investigate the fascinating electronic states in the ultra-thin cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Two-moment Neutrino Flavor Transformation with Applications to the Fast Flavor Instability in Neutron Star Mergers

Abstract Multi-messenger astrophysics has produced a wealth of data with much more to come in the future. This enormous data set will reveal new insights into the physics of core-collapse supernovae, neutron star mergers, and many other objects where it is actually possible, if not probable, that new physics is in operation. To tease out different possibilities, we will need to analyze signals from photons, neutrinos, gravitational waves, and chemical elements. This task is made all the more difficult when it is necessary to evolve the neutrino component of the radiation field and associated quantum-mechanical property of flavor in order to model the astrophysical system of interest—a numerical challenge that has not been addressed to this day. In this work, we take a step in this direction by adopting the technique of angular-integrated moments with a truncated tower of dynamical equations and a closure, convolving the flavor-transformation with spatial transport to evolve the neutrino radiation quantum field. We show that moments capture the dynamical features of fast flavor instabilities in a variety of systems, although our technique is by no means a universal blueprint for solving fast flavor transformation. To evaluate the effectiveness of our moment results, we compare to a more precise particle-in-cell method. Based on our results, we propose areas for improvement and application to complementary techniques in the future.

Astronomy & Astrophysics↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
DOE OSTI2020

An extended moments model of quantum efficiency for metals and semiconductors

The complexity of photocathode designs and detector materials, and the need to model their performance for short pulse durations, response to high frequency photons, presence of coatings and/or thinness of the absorptive layer, necessitates modifications to three-step and moments models of photoemission that are used in simulation codes. Here, methods to include input from computationally intensive approaches, such as density functional theory to model optical properties and transfer matrix approaches to treat emission from the surface or transport past coatings, by means of parametric models are demonstrated. First, a technique to accurately represent optical behavior so as to model reflectivity and penetration depth is given. Second, modifications to bulk models arising from the usage of thin film architectures, and a means to rapidly calculate them, is provided. Third, a parameterization to model the impact of wells associated with coatings and surface layers on the transmission probably is given. In all cases, the methods are computationally efficient and designed to allow for including input from numerically intensive approaches that would otherwise be unavailable for simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

In situ preparation of visible-light-driven carbon quantum dots/NaBiO 3 hybrid materials for the photoreduction of Cr(VI)

Here, different carbon quantum dots (CQDs)/NaBiO 3 hybrid materials were synthesized as photocatalysts to effectively utilize visible light for the photocatalytic degradation of contaminants effectively. These hybrid materials exhibit an enhanced photocatalytic reduction of hexavalent chromium (Cr(VI)) in the aqueous medium. Zero-dimensional nanoparticles of CQDs were embedded within the two-dimensional NaBiO 3 nanosheets by the hydrothermal process. Compared with that of the pure NaBiO 3 nanosheets, the photocatalytic performance of the hybrid catalysts was significantly high and 6 wt.% CQDs/NaBiO 3 catalyst exhibited better photocatalytic performance. We performed the first-principles density functional theory calculations to study the interfacial properties of pure NaBiO 3 nanosheets and hybrid photocatalysts, and confirmed the CQDs played an important role in the CQDs/NaBiO 3 composites. The experimental results indicated that the enhanced reduction of Cr(VI) was probably due to the high loading of CQDs (electron acceptor) on NaBiO 3 , which made NaBiO 3 nanomaterials to respond in visible light and significantly improved their electron-hole separation efficiency.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗
DOE OSTI2022

In situ detection of RF breakdown on microfabricated surface ion traps

We report microfabricated surface ion traps are a principal component of many ion-based quantum information science platforms. The operational parameters of these devices are pushed to the edge of their physical capabilities as the experiments strive for increasing performance. When the applied radio-frequency (RF) voltage is increased excessively, the devices can experience damaging electric discharge events known as RF breakdown. We introduce two novel techniques for in situ detection of RF breakdown, which we implemented while characterizing the breakdown threshold of surface ion traps produced at Sandia National Laboratories. In these traps, breakdown did not always occur immediately after increasing the RF voltage, but often minutes or even hours later. This result is surprising in the context of the suggested mechanisms for RF breakdown in vacuum. Additionally, the extent of visible damage caused by breakdown events increased with the applied voltage. To minimize the probability for damage when RF power is first applied to a device, our results strongly suggest that the voltage should be ramped up over the course of several hours and monitored for breakdown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1971

Radioactive transitions in the helium isoelectronic sequence

The principles of the atomic spectrum theory are used to quantitatively analyze radiation transitions in two-electron helium-like atomic systems. Quantum theoretical methods, describing absorption and emission of a single photon in a radiative transition between two stationary states of an atomic system, reproduced the energy level diagram for the low lying states of helium. Reliable values are obtained from accurate variationally determined two-electron nonrelativistic wave functions for radiative transition probabilities of 2 3p states in the helium isoelectric sequence, and for the 2 1s and 2 3s1 states of the helium sequence.

Dalgarno, A.↗
DOE OSTI2025

Optimizing temperature distributions for training neural quantum states using parallel tempering

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.

Neural network simulations↗
DOE OSTI2022

Exponential Escape Rate of Filamentary Incubation in Mott Spiking Neurons

Mott materials such as vanadium oxides, when subject to a strong applied voltage, present an inhomogeneous insulator-to-metal transition with formation of metallic filaments within the insulating bulk. This property is enabling the development of compact and power-efficient neuromorphic devices known as Mott neurons. However, the nature of the transition has not been fully understood yet, as it may be attributed to different effects, including Joule self-heating and hot-carrier injection. Moreover, the experimental determination of the threshold voltage needed to induce the transition has proven to be challenging, as the transition becomes increasingly unpredictable when the threshold is approached. The physical understanding of these issues would not only deepen our understanding of Mott insulators, but would also be an important step toward the realization of neuromorphic devices based on such materials. In this work we use numerical simulations based on the Mott resistor network model to study the nature of the filament incubation and formation process. Here, we show that both electronic and thermal effects, in the form of current density focusing and Joule self-heating, respectively, contribute to the filamentary incubation and growth. Remarkably, we find that the percolation of the metallic filaments near the threshold is intrinsically stochastic, qualitatively similar to the familiar Arrhenius activated behavior and to the stochastic firing of biological neurons. More precisely, we characterize the filament percolation as a Poisson point process, which has the same probability distribution as mathematical models of neuronal firing with an exponential escape rate. Finally, we support the numerical simulation results by performing experiments in VO 2 that are in agreement with the exponential escape rate behavior. Thus, we establish a functionality of Mott insulators that opens a path toward implementing neuromorphic hardware with quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Wormhole calculus, replicas, and entropies

We investigate contributions of spacetime wormholes, describing baby universe emission and absorption, to calculations of entropies and correlation functions, for example those based on the replica method. We find that the rules of the “wormhole calculus”, developed in the 1980s, together with standard quantum mechanical prescriptions for computing entropies and correlators, imply definite rules for limited patterns of connection between replica factors in simple calculations. These results stand in contrast with assumptions that all topologies connecting replicas should be summed over, and call into question the explanation for the latter. In a “free” approximation baby universes introduce probability distributions for coupling constants, and we review and extend arguments that successive experiments in a “parent” universe increasingly precisely fix such couplings, resulting in ultimately pure evolution. Once this has happened, the nontrivial question remains of how topology-changing effects can modify the standard description of black hole information loss.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗