Hamiltonian learning from time dynamics using variational algorithms

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The time propagation is implemented through Trotterization and optimized variationally with gradients computed on the quantum circuit. We validate our output by reproducing the dynamics of unseen observables on a randomly chosen state not used for the optimization. Unlike the existing techniques that try and exploit the structure/properties of the Hamiltonian, our scheme is general and provides freedom with regard to what observables or initial states can be used while still remaining efficient with regard to implementation. We extend our protocol to doing quantum state learning where we solve the reverse problem of doing state learning given time series data of observables generated against several Hamiltonian dynamics. We show results on Hamiltonians involving XX, ZZ couplings along with transverse field Ising Hamiltonians and propose an analytical method for the learning of Hamiltonians consisting of generators of the SU(3) group. This paper is likely to pave the way toward using Hamiltonian learning for time series prediction within the context of quantum machine learning algorithms.Comment: 33 pages, 18 figure

Recombination of N Atoms in a Manifold of Electronic States Simulated by Time-Reversed Nonadiabatic Photodissociation Dynamics of N2

peer reviewe

Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition.

peer reviewedWe report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters

On the Energy-specific Photodissociation Pathways of 14N2 and 14N15N Isotopomers to N Atoms of Different Reactivity: A Quantum Dynamical Perspective

peer reviewedPhotodissociation of the nitrogen molecule in the vacuum ultraviolet (VUV) is a major source of reactive nitrogen atoms in the upper atmosphere of Earth and throughout the solar system. Recent experimental studies have revealed strong energy dependence of the VUV photodissociation branching ratios to the N(4S3/2)+N(2D J ) and N(4S3/2)+N(2P J ) product channels, the primary dissociation pathways in the 108,000–116,000 cm−1 energy region. This produces N(2D J ) and N(2P J ) excited atoms that differ significantly in their chemical reactivity. The branching ratios oscillate with increase in the VUV excitation energy. We use high-level ab initio quantum chemistry to compute the potential curves of 17 electronic excited states and their nonadiabatic and spin–orbit couplings. The dynamics follow the sequential evolution from the optically excited but bound singlets. Spin–orbit coupling enables transfer to the dissociative triplet and quintet states. We compute the photodissociation yields through the dense manifold of electronic states leading to both exit channels. The dynamical simulations accurately capture the branching oscillations and enable a detailed look into the photodissociation mechanism. The major contribution to the dissociation is through the two lowest 3Π u states. However, for both isotopomers, at about 110,000 cm−1 there is an abnormally low dissociation rate into the N(4S3/2)+N(2P J ) channel that enables comparable participation of triplet and quintet 5Π u electronic states. This leads to the first peak in the branching ratio. At higher energies, trapping of the population in the 33Π u bound triplet state occurs. This favors dissociation to the lower-energy N(4S3/2)+N(2D J ) channel and results in the observed second switch in branching ratios

Time-Frequency Signatures of Electronic Coherence of Colloidal CdSe Quantum Dot Dimer Assemblies Probed at Room Temperature by Two-Dimensional Electronic Spectroscopy

Electronic coherence signatures can be directly identified in the time-frequency maps measured in two-dimensional electronic spectroscopy (2DES). Here, we demonstrate the theory and discuss the advantages of this approach via the detailed application to the fast-femtosecond beatings of a wide variety of electronic coherences in ensemble dimers of quantum dots (QDs), assembled from QDs of 3 nm in diameter, with 8% size dispersion in diameter. The observed and computed results can be consistently characterized directly in the time-frequency domain by probing the polarization in the 2DES setup. The experimental and computed time-frequency maps are found in very good agreement, and several electronic coherences are characterized at room temperature in solution, before the extensive dephasing due to the size dispersion begins. As compared to the frequency-frequency maps that are commonly used in 2DES, the time-frequency maps allow exploiting electronic coherences without additional post-processing and with fewer 2DES measurements. Towards quantum technology applications, we also report on the modeling of the time-frequency photocurrent response of these electronic coherences, which paves the way to integrating QD devices with classical architectures, thereby enhancing the quantum advantage of such technologies for parallel information processing at room temperature

Quantitating Cell–Cell Interaction Functions with Applications to Glioblastoma Multiforme Cancer Cells

We report on a method for quantitating the distance dependence of cell–cell interactions. We employ a microchip design that permits a multiplex, quantitative protein assay from statistical numbers of cell pairs, as a function of cell separation, with a 0.15 nL volume microchamber. We interrogate interactions between pairs of model brain cancer cells by assaying for six functional proteins associated with PI3k signaling. At short incubation times, cells do not appear to influence each other, regardless of cell separation. For 6 h incubation times, the cells exert an inhibiting influence on each other at short separations and a predominately activating influence at large separation. Protein-specific cell–cell interaction functions are extracted, and by assuming pairwise additivity of those interactions, the functions are shown to correctly predict the results from three-cell experiments carried out under the identical conditions

Raman-guided subcellular pharmaco-metabolomics for metastatic melanoma cells

Non-invasively probing metabolites within single live cells is highly desired but challenging. Here we utilize Raman spectro-microscopy for spatial mapping of metabolites within single cells, with the specific goal of identifying druggable metabolic susceptibilities from a series of patient-derived melanoma cell lines. Each cell line represents a different characteristic level of cancer cell de-differentiation. First, with Raman spectroscopy, followed by stimulated Raman scattering (SRS) microscopy and transcriptomics analysis, we identify the fatty acid synthesis pathway as a druggable susceptibility for differentiated melanocytic cells. We then utilize hyperspectral-SRS imaging of intracellular lipid droplets to identify a previously unknown susceptibility of lipid mono-unsaturation within de-differentiated mesenchymal cells with innate resistance to BRAF inhibition. Drugging this target leads to cellular apoptosis accompanied by the formation of phase-separated intracellular membrane domains. The integration of subcellular Raman spectro-microscopy with lipidomics and transcriptomics suggests possible lipid regulatory mechanisms underlying this pharmacological treatment. Our method should provide a general approach in spatially-resolved single cell metabolomics studies