Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXPECTATION VALUE”

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 73 records · Page 4

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗

Measurement of the CP properties of Higgs boson interactions with $\tau$-leptons with the ATLAS detector

A study of the charge conjugation and parity ($CP$) properties of the interaction between the Higgs boson and $\tau$-leptons is presented. The study is based on a measurement of $CP$-sensitive angular observables defined by the visible decay products of $\tau$-leptons produced in Higgs boson decays. The analysis uses 139 fb -1 of proton–proton collision data recorded at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV with the ATLAS detector at the Large Hadron Collider. Contributions from $\tau$-violating interactions between the Higgs boson and $\tau$-leptons are described by a single mixing angle parameter Φ $\tau$ in the generalised Yukawa interaction. Without constraining the $H$ $\rightarrow$ $\tau$$\tau$ signal strength to its expected value under the Standard Model hypothesis, the mixing angle Φ $\tau$ is measured to be 9° ± 16°, with an expected value of 0° ± 28° at the 68% confidence level. The pure $CP$-odd hypothesis is disfavoured at a level of 3.4 standard deviations. The results are compatible with the predictions for the Higgs boson in the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A technical analog of the cosmological constant problem and a solution thereof

The near vanishing of the cosmological constant is one of the most puzzling open problems in theoretical physics. We consider a system, the so-called framid, that features a technically similar problem. Its stress-energy tensor has a Lorentz-invariant expectation value on the ground state, yet there are no standard, symmetry-based selection rules enforcing this, since the ground state spontaneously breaks boosts. We verify the Lorentz invariance of the expectation value in question with explicit one-loop computations. These, however, yield the expected result only thanks to highly nontrivial cancellations, which are quite mysterious from the low-energy effective theory viewpoint.

79 ASTRONOMY AND ASTROPHYSICS↗

On the holographic dual of a symmetry operator at finite temperature

Topological symmetry operators of holographic large 𝑁 CFT 𝐷 ’s are dual to dynamical branes in the gravity dual AdS 𝐷+1 . We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFT 𝐷 and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of 0-form symmetry operators in the CFT 𝐷 are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS 3 , duality/triality defects in four-dimensional 𝒩 = 4 super Yang-Mills theory, and the dual of R-symmetry operators probing five-dimensional Bogomol’nyi–Prasad–Sommerfield black holes.

Anomalies↗

Dawn Ion Propulsion System - Initial Checkout After Launch

The first 80 days after launch of the Dawn mission were dedicated to the checkout of the spacecraft with a major emphasis on the ion propulsion system. All three ion thrusters, all three thruster-gimbal assemblies, both power processor units, both digital interface and control units, and the entire xenon feed system were completely checked out and every component was found to be in good health. Direct thrust measurements agreed well with preflight expected values for all three thrusters over the entire throttle range. Thruster electrical operating parameters and power processor units efficiencies also agreed well with preflight expected values based on acceptance test data. Two of the three ion thrusters were fully checked out within 30 days after launch. Checkout of all three thrusters was completed 64 days after launch. Deterministic thrusting with the IPS began on December 17, 2007.

electric propulsion↗

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Variational neural network approach to QFT in the field basis

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.

Klein-Gordon model↗

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

ABSTRACT We study the connection of matter density and its tracers from the probability density function (PDF) perspective. One aspect of this connection is the conditional expectation value 〈δtracer|δm〉 when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogues we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For haloes hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of 〈δtracer|δm〉 at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, i.e. the scatter of tracer density around 〈δtracer|δm〉. It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data.

Friedrich, Oliver↗

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗

Using Quasiparticle Poisoning To Detect Photons

According to a proposal, a phenomenon associated with excitation of quasiparticles in certain superconducting quantum devices would be exploited as a means of detecting photons with exquisite sensitivity. The phenomenon could also be exploited to perform medium-resolution spectroscopy. The proposal was inspired by the observation that Coulomb blockade devices upon which some quantum logic gates are based are extremely sensitive to quasiparticles excited above the superconducting gaps in their leads. The presence of quasiparticles in the leads can be easily detected via the charge states. If quasiparticles could be generated in the leads by absorption of photons, then the devices could be used as very sensitive detectors of electromagnetic radiation over the spectral range from x-rays to submillimeter waves. The devices in question are single-Cooper-pair boxes (SCBs), which are mesoscopic superconducting devices developed for quantum computing. An SCB consists of a small superconducting island connected to a reservoir via a small tunnel junction and connected to a voltage source through a gate capacitor. An SCB is an artificial two-level quantum system, the Hamiltonian of which can be controlled by the gate voltage. One measures the expected value of the charge of the eigenvectors of this quantum system by use of a radio-frequency single-electron transistor. A plot of this expected value of charge as a function of gate voltage resembles a staircase that, in the ideal case, consists of steps of height 2 e (where e is the charge of one electron). Experiments have shown that depending on the parameters of the device, quasiparticles in the form of "broken" Cooper pairs present in the reservoir can tunnel to the island, giving rise to steps of 1 e. This effect is sometimes called "poisoning." Simulations have shown that an extremely small average number of quasiparticles can generate a 1-e periodic signal. In a device according to the proposal, this poisoning would be turned to advantage. Depending on the wavelength, an antenna or other component would be used to couple radiation into the reservoir, wherein the absorption of photons would break Cooper pairs, thereby creating quasiparticles that, in turn, would tunnel to the island, creating a 1-e signal. On the basis of conservative estimates of device parameters derived from experimental data and computational simulations that fit the data, it has been estimated that the noise equivalent power of a device according to the proposal could be as low as 6 10(exp -22) W/Hz(exp 1/2). It has also been estimated that the spectroscopic resolution (photon energy divided by increment of photon energy) of such a device in visible light would exceed 100.

Echternach, Pierre↗

Uranium Single Particle Analysis for Simultaneous Fluorine and Uranium Isotopic Determinations via Laser-Induced Breakdown Spectroscopy/Laser Ablation–Multicollector–Inductively Coupled Plasma–Mass Spectrometry

Uranyl fluoride (UO 2 F 2 ) particles (<20 μm) were subjected to first-of-its-kind analysis via simultaneous laser-induced breakdown spectroscopy (LIBS) and laser ablation multi-collector inductively coupled plasma–mass spectrometry (LA–MC–ICP–MS). Briefly, a nanosecond pulsed high-energy laser was focused onto the sample (particle) surface. In a single laser pulse, the UO 2 F 2 particle was excited/ionized within the microplasma volume, and the emission of light was collected via fiber optics such that emission spectroscopy could be employed for the detection of uranium (U) and fluorine (F). The ablated particle was simultaneously transported into the MC–ICP–MS for high precision isotopic (i.e., 234 U, 235 U, and 238 U) analysis. This method, LIBS/LA–MC–ICP–MS was optimized and employed to rapidly measure 80+ UO 2 F 2 particles, which were subjected to different calcination processes, which results in varying degrees of F loss from the individual particles. In measuring the particles, the average F/U ratios for the populations treated at 100 and 500 °C were 2.78 ± 1.28 and 1.01 ± 0.50, respectively, confirming loss of F through the calcination process. The average 235 U/ 238 U on the particle populations for the 100 and 500 °C were 0.007262 (22) and 0.007231 (23), which was determined to be <0.2% from the expected value. The 234 U/ 238 U ratios on the same particles were 0.000053 (11) and 0.000050 (10) for the 100 and 500 °C, respectively, <10% from the expected value. Notably, each population was analyzed in under 5 min, demonstrating the truly rapid analysis technique presented here in this paper.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

A Risk-Averse Approach for Distribution Grid Expansion Planning

Recent episodes of natural disasters have challenged the resilience of power grids. Adequate distribution grid planning that properly captures the risk aversion of the utility system planner is a key factor to increase the flexibility of distribution networks to circumvent these events. In this paper, we propose a methodology to determine the optimal portfolio of investments in lines and storage devices in order to minimize a convex combination between expected value and CVaR of operational costs, including energy not served, while taking into account the multistage nature of the energy storage management within this context. While the expected value of energy not served has been traditionally employed to tackle routine failures, we also minimize the CVaR of energy not served to address high-impact, low-probability (HILP) events. We illustrate the performance of the proposed methodology with a 54-Bus system test case.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Spurious symptom reduction in fault monitoring

Previous work accomplished on NASA's Faultfinder concept suggested that the concept was jeopardized by spurious symptoms generated in the monitoring phase. The purpose of the present research was to investigate methods of reducing the generation of spurious symptoms during in-flight engine monitoring. Two approaches for reducing spurious symptoms were investigated. A knowledge base of rules was constructed to filter known spurious symptoms and a neural net was developed to improve the expectation values used in the monitoring process. Both approaches were effective in reducing spurious symptoms individually. However, the best results were obtained using a hybrid system combining the neural net capability to improve expectation values with the rule-based logic filter.

Shontz, William D.↗

Drop Shapes Versus Fall Velocities in Rain: 2 Contrasting Examples

Rainfall retrievals from polarimetric radar measurements require the knowledge of four fundamental rain microstructure parameters, namely, drop size distribution, drop shape distribution, canting angles and drop fall velocities. Some recent measurements of all four parameters in natural rain are summarized in [1]. In this paper, we perform an in-depth analysis of two events, using two co-located 2D video disdrometers (2DVD; see [2]) both with high calibration accuracy, and a C-band polarimetric radar [3], located 15 km away. The two events, which occurred 7 days apart (on the 18th and the 25th of Dec 2009), had moderate-to-intense rainfall rates, but the second event had an embedded convection line within the storm. The line had passed over the 2DVD site, thus enabling the shapes and fall velocities to be determined as the line crossed the site. The first event was also captured in a similar manner by both the 2DVDs as well as the C-band radar. Drop fall velocity measurements for, say, the 3 mm drops show noticeable differences between the two events. Whereas for the first event, the velocity distribution showed a narrow and symmetric distribution, with a mode at the expected value (7.95 m/s, as given by the formula in [4]), the second event produced a wider distribution with a significant skewness towards lower velocities (although its mode too was close to the expected value). Moreover, the slower 3 mm drops in the second event occurred when the convection line was directly over the 2DVD site (03:35-03:45 utc), and not before nor after. A similar trend was observed in terms of the horizontal dimensions of the 3 mm drops, i.e. large fluctuations during the same time period, but not outside the period. Vertical dimensions of the drops also fluctuated but not to the same extent. Interestingly, the horizontal dimensions tended towards larger values during the 10-minute period, implying an increase in drop oblateness, which in turn indicates the possibility of the horizontal mode oscillation, one of the three fundamental modes of drop oscillations [5], albeit the most difficult one to excite.

Thurai, M.↗

Infrared to x-ray spectral energy distributions of high redshift quasars

We have observed 14 quasars with z greater than 2.8 with the ROSAT-PSPC, and detected 12 of them, including the z=4.11 quasar 0000-263. We present the first x-ray spectrum of a radio quiet quasar with z greater than 3, 1946+768. Its x-ray spectrum is consistent with a power law with spectral index alpha(sub E)=1.8(sup +2.1, sub -1.4) and no evidence for absorption in excess of the galactic column (alpha(sub E)=1.00(sup +0.28, sub -0.32) assuming N(sub H)=N(sub H)(Gal)). A Position Sensitive Proportional Counter (PSPC) hardness ratio is used to constrain the x-ray spectral properties of the quasars for which there were less than 100 photons detected. For the radio quiet quasars, (alpha(sub E)) approximately equals 1.2, if one assumes that there is no absorption in excess of the galactic column. We combine the x-ray data with new ground based optical and near-IR spectrophotometry obtained at the Steward 2.3 m and Multiple Mirror Telescope, and data from the literature. The spectral energy distributions are compared to those of low redshift objects. For the radio quiet quasars with z greater than 2.5, the mean (alpha(sub ox)) is approximately 1.8. This is larger than the mean for quasars with z less than 2.5, but consistent with the expected value for quasars with the high optical luminosities of the objects in this sample. For the radio-loud quasars, (alpha(sub ox)) is approximately 1.4, independent of redshift. This is smaller than the expected value for the optically luminous, high redshift objects in this sample, if they are mostly GHz peaked radio sources and hence comparable to steep-spectrum, compact radio sources at lower redshift. Finally, we compare the spectral energy distributions of two representative objects to the predicted spectrum of a thin accretion disk in the Kerr geometry, and discuss the uncertainties in deriving black hole masses and mass accretion rates.

Bechtold, Jill↗

Real classical shadows

Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis $\mathcal{W}$ after it has evolved under a unitary transformation randomly sampled from a chosen distribution $\mathcal{U}$. In this work we study the case where $\mathcal{U}$ corresponds to either local or global orthogonal Clifford gates, and $\mathcal{W}$ consists of real-valued vectors. Our results show that for various situations of interest, this ‘real’ classical shadow protocol improves the sample complexity over the standard scheme based on general Clifford unitaries. For example, when one is interested in estimating the expectation values of arbitrary real-valued observables, global orthogonal Cliffords typically decrease the required number of samples by a factor of two. More dramatically, for k-local observables composed only of real-valued Pauli operators, sampling local orthogonal Cliffords leads to a reduction by an exponential-in-k factor in the sample complexity over local unitary Cliffords. Finally, we show that by measuring in a basis containing complex-valued vectors, orthogonal shadows can, in the limit of large system size, exactly reproduce the original unitary shadows protocol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gauge invariance and color charge fluctuations

The nature of confinement is connected with color charge. Unfortunately, the color charge densities in QCD, the Noether charge densities associated with the global color invariance, are not invariant under local color rotations. This implies that the expectation values of the net color charge in any region of any physical state in QCD—states that satisfy the color Gauss law—are automatically zero for all components of color. In this Letter, it is shown that the expectation value of the square of the net color charge in a region—a measure of the color charge fluctuations—is necessarily nonzero when evaluated in physical states and the result, while depending on the scheme and scale by which the theory is regulated, is gauge invariant. This holds despite the formal lack of gauge invariance of the operator. Moreover, there is a particular combination of the color charge fluctuations for the vacuum and for a system describable by a nontrivial density matrix that is independent that has a well-defined continuum limit.

color confinement↗