SEARCH · Engineering Papers

Results for “quantum state complexity”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Self-consistent Quantum Iteratively Sparsified Hamiltonian Algorithm (SQuISH)

Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware.

Diana Chamaki↗

NASA NTRS2009

Computer Code for Nanostructure Simulation

Due to their small size, nanostructures can have stress and thermal gradients that are larger than any macroscopic analogue. These gradients can lead to specific regions that are susceptible to failure via processes such as plastic deformation by dislocation emission, chemical debonding, and interfacial alloying. A program has been developed that rigorously simulates and predicts optoelectronic properties of nanostructures of virtually any geometrical complexity and material composition. It can be used in simulations of energy level structure, wave functions, density of states of spatially configured phonon-coupled electrons, excitons in quantum dots, quantum rings, quantum ring complexes, and more. The code can be used to calculate stress distributions and thermal transport properties for a variety of nanostructures and interfaces, transport and scattering at nanoscale interfaces and surfaces under various stress states, and alloy compositional gradients. The code allows users to perform modeling of charge transport processes through quantum-dot (QD) arrays as functions of inter-dot distance, array order versus disorder, QD orientation, shape, size, and chemical composition for applications in photovoltaics and physical properties of QD-based biochemical sensors. The code can be used to study the hot exciton formation/relation dynamics in arrays of QDs of different shapes and sizes at different temperatures. It also can be used to understand the relation among the deposition parameters and inherent stresses, strain deformation, heat flow, and failure of nanostructures.

Filikhin, Igor↗

NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗

NASA NTRS1989

A high level Ab initio study of the anionic hydrogen-bonded complexes FH-CN-, FH-NC-, H2O-CN- and H2O-NC-

HF, H2O, CN- and their hydrogen-bonded complexes were studied using state-of-the-art ab initio quantum mechanical methods. A large Gaussian one particle basis set consisting of triple zeta plus double polarization plus diffuse s and p functions (TZ2P + diffuse) was used. The theoretical methods employed include self consistent field, second order Moller-Plesset perturbation theory, singles and doubles configuration interaction theory and the singles and doubles coupled cluster approach. The FH-CN- and FH-NC- and H2O-CN-, H2O-NC- pairs of complexes are found to be essentially isoenergetic. The first pair of complexes are predicted to be bound by approx. 24 kcal/mole and the latter pair bound by approximately 15 kcal/mole. The ab initio binding energies are in good agreement with the experimental values. The two being shorter than the analogous C-N hydrogen bond. The infrared (IR) spectra of the two pairs of complexes are also very similar, though a severe perturbation of the potential energy surface by proton exchange means that the accurate prediction of the band center of the most intense IR mode requires a high level of electronic structure theory as well as a complete treatment of anharmonic effects. The bonding of anionic hydrogen-bonded complexes is discussed and contrasted with that of neutral hydrogen-bonded complexes.

Lee, Timothy J.↗

NASA NTRS1989

A high-level ab initio study of the anionic hydrogen-bonded complexes FH-CN(-), FH-NC(-), H2O-CN(-), and H2O-NC(-)

Lee, Timothy J.↗

NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum-mechanical theories of collision-induced electronic transitions. Within the two-state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases have been considered: (1) the avoided crossing between two potential surfaces, and (2) the spin-orbit interaction due to a 2P halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗

NASA NTRS2017

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Quantum Annealing↗

NASA NTRS1989

Direct calculation of the reactive transition matrix by L-squared quantum mechanical variational methods with complex boundary conditions

A new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities is presented. The reformulation involves solving directly for the transition matrix rather than the reactance mtrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. The convergence of calculations with real and complex boundary conditions are compared for H + H2 - H2 + H, O + H2 - OH + H, and O + HD - OH + D and OD + H.

Sun, Yan↗

NASA NTRS2001

Tunable Far Infrared Studies in Support of Stratospheric Measurements

This report summarizes research done under NASA Grant NAG5-4653. The research performed under this grant has been a collaboration between institutions including the Smithsonian Astrophysical Observatory, the National Institute of Standards and Technology, the University of Oregon, and the NASA Langley Research Center. The program has included fully line-resolved measurements of submillimeter and far infrared spectroscopic line parameters (pressure broadening coefficients and their temperature dependences, and line positions) for the analysis of field measurements of stratospheric constituents, far infrared database improvements, and studies for improved satellite measurements of the Earth's atmosphere. This research program is designed to enable the full utilization of spectra obtained in far infrared/submillimeter field measurements, such as FIRS-2, FILOS, IBEX, SLS, EosMLS, and proposed European Space Agency measurements of OH (e.g., PIRAMHYD and SFINX) for the retrieval of accurate stratospheric altitude profiles of key trace gases involved in ozone layer photochemistry. For the analysis of the spectra obtained in the stratosphere from far infrared measurements it is necessary to have accurate values of the molecular parameters (line positions, strengths, and pressure broadening coefficients) for the measured molecules and for possible interfering species. Knowledge of line positions is in increasingly good shape, with some notable exceptions. The increase in position information includes research that has been performed in the present program of research on HO2, H2O, H2O2, O3, HCl, HF, HBr, HI, CO, OH, and ClO. Examples where further line position studies are necessary include hot band and minor isotopomer lines of some of the major trace species (H2O, O3) and normal lines of some triatomic and larger molecules (NO2). Knowledge of strengths is in generally good shape, since most of the lines are from electric dipole transitions whose intensities are well determined from Stark effect measurements; exceptions include some molecules with large vibration-rotation interactions (NO2) and internal motions (H2O2 above the lowest torsional state). The line parameters that are still the least well determined are pressure broadening coefficients, and their temperature coefficients, These are strongly dependent on the quantum states involved in the transitions, in a way that is much more complex than the simple projection by directional cosine matrix elements involved in determination of rotational line strengths from static dipole moments. The following molecules have now been measured or detected in the atmosphere using far infrared and millimeter-wave emission spectroscopy from balloon- and satellite-borne spectrometers: OH, HO2, H2O (including minor isotopomers and hot band lines), H2O2, O3P, O2 (including minor isotopomers), O3 (including minor isotopomers and hot band lines), HOCl, HCl, HF, HBr, CIO, CO, CO2, N2O, NO2, N2O5, HNO3, ClNO3, and HCN. Many of these species have spectral lines that are saturated in stratospheric spectra. In these cases, the measured line equivalent widths are proportional to (line strength x Lorentz width) (exp 1/2) so that the pressure broadening coefficients are as important as the line intensities in determining concentration profiles. Interpretation of field measurements for these species have required ongoing measurement programs of pressure broadening measurements. Other species (HO2, HGCl, H2O2, HBr, and NO2, as examples) have required further line position studies in order to fully analyze the field measurements.

Chance, Kelly V.↗

NASA NTRS2011

Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

coherence theory↗

NASA NTRSDate not supplied

Planning for Compilation of a Quantum Algorithm for Graph Coloring

Recently, the problem of compiling general quantum algorithms for implementation on near-term quantum processors has been introduced to the AI community. Previous work demonstrated that temporal planning is an attractive approach for part of this compilation task, specifically, the routing of circuits that implement the Quantum Alternating Operator Ansatz (QAOA) applied to theMaxCut problem on a quantum processor architecture. In this paper, we extend the earlier work to route circuits that implement QAOAfor Graph Coloring problems. QAOA for coloring requires execution of more, and more complex, operations on the chip, which makes routing a more challenging problem. We evaluate the approach on state-of-the-art hardware architectures from leading quantum computing companies. Additionally, we investigate applying the planning approach to qubit initialization as well as routing. Our empirical evaluation shows that temporal planning compares well to reasonable analytic upper bounds [20], and that solving qubit initialization with a classical planner generally helps temporal planners in finding shorter-makespan compilations for QAOA for Graph Coloring.These advances suggest that temporal planning can be an effective approach for more complex quantum computing algorithms and architectures.

Minh Do↗

NASA NTRS1991

Calculations on the rate of the ion-molecule reaction between NH3(+) and H2

The rate coefficient for the ion-molecule reaction NH3(+) + H2 yields NH4(+) + H has been calculated as a function of temperature with the use of the statistical phase space approach. The potential surface and reaction complex and transition state parameters used in the calculation have been taken from ab initio quantum chemical calculations. The calculated rate coefficient has been found to mimic the unusual temperature dependence measured in the laboratory, in which the rate coefficient decreases with decreasing temperature until 50-100 K and then increases at still lower temperatures. Quantitative agreement between experimental and theoretical rate coefficients is satisfactory given the uncertainties in the ab initio results and in the dynamics calculations. The rate coefficient for the unusual three-body process NH3(+) + H2 + He yields NH4(+) + H + He has also been calculated as a function of temperature and the result found to agree well with a previous laboratory determination.

Herbst, Eric↗

NASA NTRS1991

Incoherent vs. coherent behavior in the normal state of copper oxide superconductors

The self-consistent quantum fluctuations around the mean-field Hartree-Fock state of the Hubbard model provide a very good description of the ground state and low temperature properties of a 2-D itinerant antiferromagnet. Very good agreement with numerical calculations and experimental data is obtained by including the one- and two-loop spin wave corrections to various physical quantities. In particular, the destruction of the long-range order above the Neel temperature can be understood as a spontaneous generation of a length-scale epsilon(T), which should be identified as the spin correlation length. For finite doping, the question of the Hartree-Fock starting point becomes a more complex one since an extra hole tends to self-trap in antiferromagnetic background. Such quantum defects in an underlying antiferromagnetic state can be spin-bags or vortex-like structures and tend to suppress the long-range order. If motion of the holes occurs on a time-scale shorter than the one associated with the motion of these quantum defects of a spin background, one obtains several important empirical features of the normal state of CuO superconductors like linear T-dependence of resistivity, the cusp in the tunneling density of states, etc. As opposed to a familiar Fermi-liquid behavior, the phenomenology of the above system is dominated by a large incoherent piece of a single hole propagator, resulting in many unusual normal state properties.

Tesanovic, Zlatko↗

NASA NTRS2003

Quantum detection of coherent-state signals in the presence of noise

A general method for solving an important class of quantum detection problems will be presented and evaluated. The quantum theory for detecting pure states for communications purposes has been developed over two decades ago, however the mixed state problem representing signal plus noise states has received little attention due to its great complexity. Here we develop a practical model for solving the mixed-state problem using a discrete approximation to the coherent-state representation of signal plus noise density operators.

Quantum communication quantum detection↗

NASA NTRS2018

A Blueprint for Demonstrating Quantum Supremacy with Superconducting Qubits

Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.

Kechedzhi, Kostyantyn↗

NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗

NASA NTRS1989

High-resolution near-infrared spectroscopy of water dimer

High-resolution near-infrared spectra are reported for all of the O-H stretch vibrational bands of the water dimer. The four O-H vibrations are characterized as essentially independent proton-donor or proton-acceptor motions. In addition to the rotational and vibrational information contained in these spectra, details are obtained concerning the internal tunneling dynamics in both the ground and excited vibrational states. These results show that, for tunneling motions which involve the interchange of the proton donor and acceptor molecules, the associated frequencies decrease substantially due to vibrational excitation. The predissociation lifetimes for the various states of the dimer are determined from linewidth measurements. These results clearly show that the predissociation dynamics is strongly dependent on the tunneling states, as well as the Ka quantum number, indicating that the internal tunneling dynamics plays an important role in determining the dissociation rate in this complex.

Huang, Z. S.↗

NASA NTRS2004

Novel Biomedical Device Utilizing Light-Emitting Nanostructures Developed

Sketches and chemical diagrams of state-of-the-art device and novel proposed device are presented. Current device uses a diode laser that emits into a fluorescent fluid only one wavelength and a photodetector diode that detects only one wavelength. Only one type of bacteria can be detected. The proposed device uses a quantum dot array that emits into a fluorescent fluid multiple wavelengths and an NIR 512 spectrometer that scans 0.8- to 1.7-mm wavelengths. Hundreds of different bacteria and viruses can be detected. A novel biomedical device is being developed at the NASA Glenn Research Center in cooperation with the University of Michigan. This device uses nano-structured quantum dots that emit light in the near-infrared (IR) region. The nanostructured quantum dots are used as a source and excite fluorochrome polymers coupled with antibodies that seek out and attach to specific bacteria and viruses. The fluorochrome polymers/antibodies fluoresce at specific wavelengths in the near-IR spectrum, but these wavelengths are offset from the excitation wavelength and can be detected with a tunable spectrometer. The device will be used to detect the presence of viruses and bacteria in simple fluids and eventually in more complex fluids, such as blood. Current state-of-the-art devices are limited to single bacteria or virus detection and a considerable amount of time and effort is required to prepare samples for analysis. Most importantly, the devices are quite large and cumbersome, which prohibits them from being used on the International Space Station and the space shuttles. This novel device uses nanostructured quantum dots which, through molecular beam epitaxy and highly selective annealing processes, can be developed into an illumination source that could potentially generate hundreds of specific wavelengths. As a result, this device will be able to excite hundreds of antibody/fluorochrome polymer combinations, which in turn could be used to detect hundreds of bacteria and viruses in fluids. A novel sample preparation technique that exploits micromembrane filtration and centrifugation methods has been developed for this device. The technique greatly reduces the time required to prepare the sample and the amount of sample needed to perform an accurate and comprehensive analysis. Last, and probably most important, because of the nano-light-emitting source and the novel sample preparation technique, the overall size of the device could be reduced dramatically. This device will serve as a nanoscale lab-on-a-chip for in situ microorganism detection and will enable tests to be performed on a time scale of minutes rather than days. Thus, it is ideally suited for monitoring the environmental conditions onboard the International Space Station and the space shuttles, thereby enhancing the safety of the astronauts. In addition, the device has important commercial applications, such as detecting the presence of bacteria and viruses in water at food- and beverage-processing centers, water treatment plants, and restaurants. Also, this technology has the potential to be used to detect bacteria and viruses in more complex fluids, such as blood--which in all likelihood would revolutionize blood analysis as it is performed today. This project was made possible through the Director's Discretionary Fund and is ongoing. In addition, this project provides funding to Dr. Rachel Goldman of the University of Michigan for the research and development of nanostructured quantum dots.

Scardelletti, Maximilian C.↗