A quantum information processing machine for computing by observables.

A quantum machine that accepts an input and processes it in parallel is described. The logic variables of the machine are not wavefunctions (qubits) but observables (i.e., operators) and its operation is described in the Heisenberg picture. The active core is a solid-state assembly of small nanosized colloidal quantum dots (QDs) or dimers of dots. The size dispersion of the QDs that causes fluctuations in their discrete electronic energies is a limiting factor. The input to the machine is provided by a train of very brief laser pulses, at least four in number. The coherent band width of each ultrashort pulse needs to span at least several and preferably all the single electron excited states of the dots. The spectrum of the QD assembly is measured as a function of the time delays between the input laser pulses. The dependence of the spectrum on the time delays can be Fourier transformed to a frequency spectrum. This spectrum of a finite range in time is made up of discrete pixels. These are the visible, raw, basic logic variables. The spectrum is analyzed to determine a possibly smaller number of principal components. A Lie-algebraic point of view is used to explore the use of the machine to emulate the dynamics of other quantum systems. An explicit example demonstrates the considerable quantum advantage of our scheme.

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size.

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

Time evolution of entanglement of electrons and nuclei and partial traces in ultrafast photochemistry.

Broad in energy optical pulses induce ultrafast molecular dynamics where nuclear degrees of freedom are entangled with electronic ones. We discuss a matrix representation of wave functions of such entangled systems. Singular Value Decomposition (SVD) of this matrix provides a representation as a sum of separable terms. Their weights can be arranged in decreasing order. The representation provided by the SVD is equivalent to a Schmidt decomposition. If there is only one term or if one term is already a good approximation, the system is not entangled. The SVD also provides either an exact or a few term approximation for the partial traces. A simple example, the dynamics of LiH upon ultrafast excitation to several non-adiabatically coupled electronic states, is provided. The major contribution to the entanglement is created during the exit from the Franck Condon region. An additional contribution is the entanglement due to the nuclear motion induced non-adiabatic transitions.

Ultrafast geometrical reorganization of a methane cation upon sudden ionization: an isotope effect on electronic non-equilibrium quantum dynamics.

The ultrafast structural, Jahn-Teller (JT) driven, electronic coherence mediated quantum dynamics in the CH4+ and CD4+ cations that follows sudden ionization using an XUV attopulse exhibits a strong isotope effect. The JT effect makes the methane cation unstable in the Td geometry of the neutral molecule. Upon the sudden ionization the cation is produced in a coherent superposition of three electronic states that are strongly coupled and neither is in equilibrium with the nuclei. In the ground state of the cation the few femtosecond structural rearrangement leads first to a geometrically less distorted D2d minimum followed by a geometrical reorganization to a shallow C2v minimum. The dynamics is computed for an ensemble of 8000 ions randomly oriented with respect to the polarization of the XUV pulse. The ratio, about 3, of the CD4+ to CH4+ autocorrelation functions, is in agreement with experimental measurements of high harmonic spectra. The high value of the ratio is attributed to the faster electronic coherence dynamics in CH4+.

Electronic Coherences Steer the Strong Isotope Effect in the Ultrafast Jahn-Teller Structural Rearrangement of Methane Cation upon Tunnel Ionization.

We report on fully quantum electronic-nuclear dynamics following sudden ionization from the neutral in the three lowest electronic states of the CH4+ and CD4+ cations. There is a strong Jahn-Teller effect in the Franck-Condon region, and we employ two nuclear degrees of freedom that span the internal coordinates involved in the Jahn-Teller coupling. The initial state results from tunneling ionization by a strong IR field which coherently pumps the three lowest states of the cation, D0, D1, and D2. The quantum dynamical simulations show that a strong isotope effect occurs when the ionization significantly accesses the D2 state of the cation in the Franck-Condon region. The computed isotope effect is larger than expected on the basis of the effective mass ratio. The strong effect is due to fast oscillations of the electronic coherences between the D2 and the D1 and D0 electronic states and their modulation by the nonadiabatic couplings before a significant onset of nuclear motion. The magnitude of the effect is similar to the one that we previously reported for a sudden photoionization process. A strong isotope effect has been observed in high harmonic spectroscopy studies of the very short time dynamics Jahn-Teller structural rearrangement of the methane cation upon sudden ionization.

The density matrix via few dominant observables: The quantum interference in the isotope effect for atto-pumped N2.

Atto- and sub-femto-photochemistry enables preparation of molecules in a coherent superposition of several electronic states. Recently [Ajay et al., Proc. Natl. Acad. Sci. U. S. A. 115, 5890-5895 (2018)], we examined an effect of the nuclear mass during the non-adiabatic transfer between strongly coupled Rydberg and valence electronic states in N2 excited by an ultrafast pulse. Here, we develop and analyze an algebraic description for the density matrix and its logarithm, the surprisal, in such a superposition of states with a focus on the essentially quantum effect of mass. This allows for the identification of a few observables that accurately characterize the density matrix of the system with several coupled electron-nuclear states. We compact the time evolution in terms of time-dependent coefficients of these observables. Using the few observables, we derive an analytical expression for the time-dependent surprisal. This provides a mass-dependent phase factor only in the observables off-diagonal in the electronic index. The isotope effect is shown to be explicitly driven by the shift in the equilibrium position of the valence state potential. It is analytically given as a time-dependent phase factor describing the interference in the overlap of the two wave packets on the coupled electronic states. This phase factorizes as a product of classical and quantal contributions.

Ultrafast fs coherent excitonic dynamics in CdSe quantum dots assemblies addressed and probed by 2D electronic spectroscopy.

We show in a joint experimental and theoretical study that ultrafast femto-second (fs) electronic coherences can be characterized in semi-conducting colloidal quantum dot (QD) assemblies at room temperature. The dynamics of the electronic response of ensembles of CdSe QDs in the solution and of QD dimers in the solid state is probed by a sequence of 3 fs laser pulses as in two-dimensional (2D) electronic spectroscopy. The quantum dynamics is computed using an excitonic model Hamiltonian based on the effective mass approximation. The Hamiltonian includes the Coulomb, spin-orbit, and crystal field interactions that give rise to the fine structure splittings. In the dimers studied, the interdot distance is sufficiently small to allow for an efficient interdot coupling and delocalization of the excitons over the two QDs of the dimer. To account for the inherent few percent size dispersion of colloidal QDs, the optical response is modeled by averaging over an ensemble of 2000 dimers. The size dispersion is responsible for an inhomogeneous broadening that limits the lifetimes of the excitonic coherences that can be probed to about 150 fs-200 fs. Simulations and experimental measurements in the solid state and in the solution demonstrate that during that time scale, a very rich electronic coherent dynamics takes place that involves several types of intradot and interdot (in the case of dimers) coherences. These electronic coherences exhibit a wide range of beating periods and provide a versatile basis for a quantum information processing device on a fs time scale at room temperature.

Personalized disease signatures through information-theoretic compaction of big cancer data.

Every individual cancer develops and grows in its own specific way, giving rise to a recognized need for the development of personalized cancer diagnostics. This suggested that the identification of patient-specific oncogene markers would be an effective diagnostics approach. However, tumors that are classified as similar according to the expression levels of certain oncogenes can eventually demonstrate divergent responses to treatment. This implies that the information gained from the identification of tumor-specific biomarkers is still not sufficient. We present a method to quantitatively transform heterogeneous big cancer data to patient-specific transcription networks. These networks characterize the unbalanced molecular processes that deviate the tissue from the normal state. We study a number of datasets spanning five different cancer types, aiming to capture the extensive interpatient heterogeneity that exists within a specific cancer type as well as between cancers of different origins. We show that a relatively small number of altered molecular processes suffices to accurately characterize over 500 tumors, showing extreme compaction of the data. Every patient is characterized by a small specific subset of unbalanced processes. We validate the result by verifying that the processes identified characterize other cancer patients as well. We show that different patients may display similar oncogene expression levels, albeit carrying biologically distinct tumors that harbor different sets of unbalanced molecular processes. Thus, tumors may be inaccurately classified and addressed as similar. These findings highlight the need to expand the notion of tumor-specific oncogenic biomarkers to patient-specific, comprehensive transcriptional networks for improved patient-tailored diagnostics.

Chirality of a rhodamine heterodimer linked to a DNA scaffold: an experimental and computational study.

The chiroptical properties of multi-chromophoric systems are governed by the intermolecular arrangement of the monomeric units. We report on a computational and experimental study of the linear optical properties and supramolecular structure of a rhodamine heterodimer assembled on a DNA scaffold. The experimental absorption and circular dichroism (CD) profiles confirm the dimer formation. Computationally, starting from low-cost DFT/TDDFT simulations of the bare dimer we attribute the measured -/+ CD sign sequence of the S1/S2 bands to a specific chiral conformation of the heterodimer. In the monomers, as typical for rhodamine dyes, the electric transition dipole of the lowest π-π* transition is parallel to the long axis of the xanthene planes. We show that in the heterodimer the sign sequence of the two CD bands is related to the orientation of these long axes. To account explicitly for environment effects, we use molecular dynamics (MD) simulations for characterizing the supramolecular structure of the two optical isomers tethered on DNA. Average absorption and CD-profiles were modeled using ab initio TDDFT calculations at the geometries sampled along a few nanosecond MD run. The absorption profiles computed for both optical isomers are in good agreement with the experimental absorption spectrum and do not allow one to discriminate between them. The computed averaged CD profiles provide the orientation of monomers in the enantiomer that is dominant under the experimental conditions.

Selective bond formation triggered by short optical pulses: quantum dynamics of a four-center ring closure.

We report bond formation induced by an ultrashort UV pulse. The photochemical process is described by quantum dynamics as coherent electronic and nuclear motions during the ultrashort pulse induced ring closure of norbornadiene to quadricyclane. Norbornadiene consists of two ethylene moieties connected by a rigid (CH2)3 bridge. Upon photoexcitation, two new sigma bonds are formed, resulting in the closure of a four-atom ring. As a medium-sized polyatomic molecule, norbornadiene exhibits a high density of strongly coupled electronic states from about 6 eV above the ground state. We report on inducing the formation of the new bonds using a short femtosecond UV pulse to pump a non-equilibrium electronic density in the open form that evolves towards the closed ring form. As the coherent electronic-nuclear coupled dynamics unfold, the excited states change character through non-adiabatic interactions and become valence states for the two new C-C bonds of quadricyclane. Our three-dimensional fully quantum dynamical grid simulations during the first 200 fs show that short UV pulses of different polarization initiate markedly different initial non-equilibrium electronic densities that follow different dynamical paths to the S0/S1 conical intersection. They lead to different initial relative yields of quadricyclane, thereby opening the way to controlling bond-making with attopulses.

Surprisal of a quantum state: Dynamics, compact representation, and coherence effects.

Progress toward quantum technologies continues to provide essential new insights into the microscopic dynamics of systems in phase space. This highlights coherence effects whether these are due to ultrafast lasers whose energy width spans several states all the way to the output of quantum computing. Surprisal analysis has provided seminal insights into the probability distributions of quantum systems from elementary particle and also nuclear physics through molecular reaction dynamics to system biology. It is therefore necessary to extend surprisal analysis to the full quantum regime where it characterizes not only the probabilities of states but also their coherence. In principle, this can be done by the maximal entropy formalism, but in the full quantum regime, its application is far from trivial [S. Dagan and Y. Dothan, Phys. Rev. D 26, 248 (1982)] because an exponential function of non-commuting operators is not easily accommodated. Starting from an exact dynamical approach, we develop a description of the dynamics where the quantum mechanical surprisal, a linear combination of operators, plays a central role. We provide an explicit route to the Lagrange multipliers of the system and identify those operators that act as the dominant constraints.

Temporal and spatially resolved imaging of the correlated nuclear-electronic dynamics and of the ionized photoelectron in a coherently electronically highly excited vibrating LiH molecule.

Few-cycle ultrashort IR pulses allow excitation of coherently coupled electronic states toward steering nuclear motions in molecules. We include in the Hamiltonian the excitation process using an IR pulse of a definite phase between its envelope and carrier wave and provide a quantum mechanical description of both multiphoton excitation and ionization. We report on the interplay between these two processes in shaping the ensuing coupled electronic-nuclear dynamics in both the neutral excited electronic states and the cationic states of the diatomic molecule LiH. The dynamics is described by solving numerically the time-dependent Schrodinger equation at nuclear grid points using the partitioning technique with a subspace of ten coupled bound states and a subspace of discretized continuous states for the photoionization continua. We show that the coherent dynamics in the neutral subspace is strongly affected by the amplitude exchanges with the ionization continua during the pulse, as well as by the onset of nuclear motion. The coupling to the cation and the resulting ionization do not preclude the control of the motion in the neutral through control of the carrier-envelope phase. Our methodology provides visualization in space and in time not only of the entangled vibronic wave packet in the neutral states but also of the wave packet of the outgoing photoelectron. Thereby, we can spatially and temporally follow the dynamics of the outgoing and bound electrons during the pulse and the nuclear motion in the bound subspace while moving through nonadiabatic coupling regions after the pulse.

A Probabilistic Finite State Logic Machine Realized Experimentally on a Single Dopant Atom.

Exploiting the potential of nanoscale devices for logic processing requires the implementation of computing functionalities departing from the conventional switching paradigm. We report on the design and the experimental realization of a probabilistic finite state machine in a single phosphorus donor atom placed in a silicon matrix electrically addressed and probed by scanning tunneling spectroscopy (STS). The single atom logic unit simulates the flow of visitors in a maze whose topology is determined by the dynamics of the electronic transport through the states of the dopant. By considering the simplest case of a unique charge state for which three electronic states can be resolved, we demonstrate an efficient solution of the following problem: in a maze of four connected rooms, what is the optimal combination of door opening rates in order to maximize the time that visitors spend in one specific chamber? The implementation takes advantage of the stochastic nature of electron tunneling, while the output remains the macroscopic current whose reading can be realized with standard techniques and does not require single electron sensitivity.

Pumping and probing vibrational modulated coupled electronic coherence in HCN using short UV fs laser pulses: a 2D quantum nuclear dynamical study.

The coupled electronic-nuclear coherent dynamics induced by a short strong VUV fs pulse in the low excited electronic states of HCN is probed by transient absorption spectroscopy with a second weaker fs UV pulse. The nuclear time-dependent Schrodinger equation is solved on a 2D nuclear grid with several electronic states with a Hamiltonian including the dipole coupling to the pump and the probe electric fields. The two internal nuclear coordinates describe the motion of the light H atom. There is a band of several excited electronic states at about 8 eV above the ground state (GS) that is transiently accessed by the pump pulse. We tailored the pump so as to selectively populate the lowest 1A'' electronic state thereby the pulse creates an electronic coherence with the GS. Our simulations show that this electronic coherence is modulated by the nuclear motion and persists all the way to dissociation on the 1A'' state. Transient absorption spectra computed as a function of the delay time between the pump and the probe pulses provide a detailed probe of the electronic amplitude and its phase, as well as of the modulation of the electronic coherence by the nuclear motion, both bound and dissociative.

Low-lying, Rydberg states of polycyclic aromatic hydrocarbons (PAHs) and cyclic alkanes.

TD-DFT calculations of low-lying, Rydberg states of a series of polycyclic hydrocarbons and cyclic alkanes are presented. Systematic variations in binding energies and photoelectron angular distributions for the first members of the s, p and d Rydberg series are predicted for increasing molecular complexity. Calculated binding energies are found to be in very good agreement with literature values where they exist for comparison. Experimental angle-resolved photoelectron spectroscopy results are presented for coronene, again showing very good agreement with theoretical predictions of binding energies and also for photoelectron angular distributions. The Dyson orbitals for the small "hollow" carbon structures, cubane, adamantane and dodecahedrane, are shown to have close similarities to atomic s, p and d orbitals, similar to the superatom molecular orbitals (SAMOs) reported for fullerenes, indicating that these low-lying, diffuse states are not restricted to π-conjugated molecules.

Coherent electronic and nuclear dynamics in a rhodamine heterodimer-DNA supramolecular complex.

Elucidating the role of quantum coherences in energy migration within biological and artificial multichromophoric antenna systems is the subject of an intense debate. It is also a practical matter because of the decisive implications for understanding the biological processes and engineering artificial materials for solar energy harvesting. A supramolecular rhodamine heterodimer on a DNA scaffold was suitably engineered to mimic the basic donor-acceptor unit of light-harvesting antennas. Ultrafast 2D electronic spectroscopic measurements allowed identifying clear features attributable to a coherent superposition of dimer electronic and vibrational states contributing to the coherent electronic charge beating between the donor and the acceptor. The frequency of electronic charge beating is found to be 970 cm-1 (34 fs) and can be observed for 150 fs. Through the support of high level ab initio TD-DFT computations of the entire dimer, we established that the vibrational modes preferentially optically accessed do not drive subsequent coupling between the electronic states on the 600 fs of the experiment. It was thereby possible to characterize the time scales of the early time femtosecond dynamics of the electronic coherence built by the optical excitation in a large rigid supramolecular system at a room temperature in solution.

Quantum Nuclear Dynamics Pumped and Probed by Ultrafast Polarization Controlled Steering of a Coherent Electronic State in LiH.

The quantum wave packet dynamics following a coherent electronic excitation of LiH by an ultrashort, polarized, strong one-cycle infrared optical pulse is computed on several electronic states using a grid method. The coupling to the strong field of the pump and the probe pulses is included in the Hamiltonian used to solve the time-dependent Schrodinger equation. The polarization of the pump pulse allows us to control the localization in time and in space of the nonequilibrium coherent electronic motion and the subsequent nuclear dynamics. We show that transient absorption, resulting from the interaction of the total molecular dipole with the electric fields of the pump and the probe, is a very versatile probe of the different time scales of the vibronic dynamics. It allows probing both the ultrashort, femtosecond time scale of the electronic coherences as well as the longer dozens of femtoseconds time scales of the nuclear motion on the excited electronic states. The ultrafast beatings of the electronic coherences in space and in time are shown to be modulated by the different periods of the nuclear motion.

Probing in Space and Time the Nuclear Motion Driven by Nonequilibrium Electronic Dynamics in Ultrafast Pumped N2.

An ultrafast electronic excitation of N2 in the vacuum ultraviolet creates a nonstationary coherent linear superposition of interacting valence and Rydberg states resulting in a net oscillating dipole moment. There is therefore a linear response to an electrical field that can be queried by varying the time delay between the pump and a second optical probe pulse. Both the pump and probe pulses are included in our computation as part of the Hamiltonian, and the time-dependent wave function for both electronic and nuclear dynamics is computed using a grid representation for the internuclear coordinate. Even on an ultrafast time scale there are several processes that can be discerned beyond the expected coherence oscillations. In particular, the coupling between the excited valence and Rydberg states of the same symmetry is very evident and can be directly probed by varying the delay between pulse and probe. For quite a number of vibrations the nuclear motion does not dephase the electronic disequilibrium. However, the nuclear motion does modulate the dipolar response by taking the wave packet in and out of the Franck-Condon region and by its strong influence on the coupling of the Rydberg and valence states. A distinct isotope effect arises from the dependence of the interstate coupling on the nuclear mass.

miRNA and mRNA cancer signatures determined by analysis of expression levels in large cohorts of patients.

Toward identifying a cancer-specific gene signature we applied surprisal analysis to the RNAs expression behavior for a large cohort of breast, lung, ovarian, and prostate carcinoma patients. We characterize the cancer phenotypic state as a shared response of a set of mRNA or microRNAs (miRNAs) in cancer patients versus noncancer controls. The resulting signature is robust with respect to individual patient variability and distinguishes with high fidelity between cancer and noncancer patients. The mRNAs and miRNAs that are implicated in the signature are correlated and are known to contribute to the regulation of cancer-signaling pathways. The miRNA and mRNA networks are common to the noncancer and cancer patients, but the disease modulates the strength of the connectivities. Furthermore, we experimentally assessed the cancer-specific signatures as possible therapeutic targets. Specifically we restructured a single dominant connectivity in the cancer-specific gene network in vitro. We find a deflection from the cancer phenotype, significantly reducing cancer cell proliferation and altering cancer cellular physiology. Our approach is grounded in thermodynamics augmented by information theory. The thermodynamic reasoning is demonstrated to ensure that the derived signature is bias-free and shows that the most significant redistribution of free energy occurs in programming a system between the noncancer and cancer states. This paper introduces a platform that can elucidate miRNA and mRNA behavior on a systems level and provides a comprehensive systematic view of both the energetics of the expression levels of RNAs and of their changes during tumorigenicity.

Molecular decision trees realized by ultrafast electronic spectroscopy.

The outcome of a light-matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light-matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on-off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the time-evolving state of the bichromophoric system. The bilinear laser-system interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations.