Search NASA⌕ Search

SEARCH · Search NASA

Results for “Hadamard transform”

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.

13 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Methods of resolving artifacts in Hadamard-transformed data

Apparatus and methods are disclosed for processing data transformed according to an invertible transform (e.g., using a Hadamard transform) multiplexing scheme. In one example of the disclosed technology, a computer-implemented method includes generating transformed data by applying a Hadamard transform to intensity data generated by modulating input of analytes into a mass spectrometer according to a pseudorandom sequence (PRS). The exemplary method further includes identifying at least one pair of symmetric intensity peaks in the transformed data based on the PRS and removing data associated with the pair of symmetric peaks from the transformed data to produce modified data, which can be used to identify, characterize, and/or quantify the composition of the sample. In some examples, the exemplary method further includes validating peaks in the transformed data based on comparing the location of peaks in the untransformed intensity data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Methods of resolving artifacts in Hadamard-transformed data

A method of validating data produced from a multiplexing process on an analytical instrument is disclosed. In one embodiment, the method includes using a pseudorandom sequence to encode a multiplexed segment of data; applying Hadamard transform to generate a demultiplexed segment of the data; aligning the pseudorandom sequence to the multiplexed data; and calculating a score for at least one positive value in the demultiplexed segment to find a valid demultiplexed value.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Toward artifact-free data in Hadamard transform-based double multiplexing of ion mobility-Orbitrap mass spectrometry

The integration of ion mobility spectrometry (IMS) with trap-based mass spectrometer (MS) such as Orbitrap using the dual gate approach suffers from low duty cycle. Efforts to improve the duty cycle involve the utilization of Hadamard transform based double multiplexing which significantly improve the signal to noise ratio and duty cycle of the ion mobility – Orbitrap mass spectrometry (IM – Orbitrap MS) platform. However, significant fluctuations in ion intensity and the temporal shifts in the encoded data give rise to artifacts and noise in the demultiplexed data which significantly reduce the data quality and negate the benefits of multiplexing. We propose a new approach that identifies the true IM peaks and helps in eliminating the artifacts in the demultiplexed data leading to a decrease in false positives in subsequent data processing. The algorithm takes an analytical approach to first identify the position of the IM peak in the temporal domain, and then demultiplex and identify the true data making it easier for subsequent data processing. After the application of the algorithm, the quality of the IM-Orbitrap MS measurements was greatly improved because of the reduction in artifacts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Simultaneous Improvement of Resolving Power and Signal-to-Noise Ratio Using a Modified Hadamard Transform-Inverse Ion Mobility Spectrometry Technique

In order to improve the resolving power (RP) and signal-to-noise ratio (SNR) of ion mobility spectrometry (IMS) simultaneously, a modified Hadamard transform-inverse ion mobility spectrometry (MHT-IIMS) technique was developed. In this novel technique, a series of isolating codes were appended to each element of the pseudo random binary sequence (PRBS), and then the modified modulation sequence was formed and used to control the ion gate of the inverse IMS (IIMS). Experimental results demonstrate that the MHT-IIMS technique can significantly enhance the resolving power and SNR simultaneously by measuring the spectra of reaction ions. Furthermore, the gas sample CCl{sub 4} and CHCl{sub 3} were measured for evaluating the capability of detecting those samples which have single and multiple product ions. The results show that this novel technique is able to simultaneously improve the resolving power and SNR notablely for the real sample detection without any significant instrumental changes. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

An investigation of Newton-Sketch and subsampled Newton methods

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing

In this paper, we report the experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998±0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C band (1530–1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits, we implement a 3×3 extension of the Hadamard gate: the balanced tritter. This tritter—the first ever demonstrated for frequency modes—attains fidelity 0.9989±0.0004. Finally, these gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Bell state analyzer for spectrally distinct photons

We demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal fidelities of ∼ <#comment/> 98 % <#comment/> for discriminating between the | Ψ <#comment/> + ⟩ <#comment/> and | Ψ <#comment/> − <#comment/> ⟩ <#comment/> frequency-bin Bell states. Our approach resolves the tension between wavelength-multiplexed state transport and high-fidelity Bell state measurements, which typically require spectral indistinguishability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

In this work, we introduce the notion of combinatorial gauge symmetry—a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)—that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics

Huygens triviality – a concept invented by Jacques Hadamard – describes an equivalence class connecting those 2nd order partial differential equations which are transformable into the wave equation. In this work it is demonstrated, that the Schrödinger equation with the time-independent Hamiltonian belongs to such an equivalence class. The wave equation is the equation for which Huygens’ principle (HP) holds. The HP was a subject of confusion in both physics and mathematics literature for a long time. Not surprisingly, the role of this principle was obscured from the beginnings of quantum mechanics causing some theoretical and experimental misunderstandings. The purpose of this work is to bring the full clarity into this topic. By doing so, we obtained a large amount of new results related to uses of Lie sphere geometry, of twistors, of Dupin cyclides, of null electromagnetic fields, of AdS-CFT correspondence, of Penrose limits, of geometric algebra, etc. in physical problems ranging from the atomic to high energy physics and cosmology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum computation of nuclear observables involving linear combinations of unitary operators

Here we present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilize the Hadamard test and the linear combination of unitaries based methods to compute the expectation values. We apply these methods to calculate the electric quadrupole moment of the deuteron. The results are compared for the Jordan-Wigner transformation and Gray code encoding. We discuss the versatility of our approach that can be utilized in general to calculate several observables on a quantum computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Topological quantum computation based on chiral Majorana fermions

Here, the chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Design Methodologies for Integrated Quantum Frequency Processors

We report frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm—based on electro-optic phase modulators and Fourier-transform pulse shapers—providing a path for scalable construction of quantum gates. Yet all experimental demonstrations to date have relied on discrete fiber-optic components that occupy significant physical space and impart appreciable loss. In this article, we introduce a model for the design of quantum frequency processors comprising microring resonator-based pulse shapers and integrated phase modulators. We estimate the performance of single and parallel frequency-bin Hadamard gates, finding high fidelity values that extend to frequency bins with relatively wide bandwidths. By incorporating multi-order filter designs as well, we explore the limits of tight frequency spacings, a regime extremely difficult to obtain in bulk optics. Overall, our model is general, simple to use, and extendable to other material platforms, providing a much-needed design tool for future frequency processors in integrated photonics.

97 MATHEMATICS AND COMPUTING↗