Adiabatic Framework Research Articles

On the circuit model of two quantum adiabatic search algorithms

The early work of Wei et al. has shown that it is possible to do the computation in constant time for quantum search in quantum local adiabatic evolution framework if the system Hamiltonian has an extra enlarged factor proportional to the square-root of the size of the problem. Also in our prior work, we have shown that it is possible to apply a linear interpolating path in the system Hamiltonian to achieve an O(1) time complexity for a quantum global adiabatic computation. In this paper, we discuss the issues when implementing these two quantum algorithms on the quantum circuit model, and find that to our surprise, the time slices produced does not equal to the time complexity of the algorithm in each case. This is in contrast to the previous related results, because there these two quantities always coincide. When taking into account of the whole energy-level increase of the system compared with that of the usual quantum adiabatic evolutions and the corresponding time complexity simultaneously, we find that the time slices needed always consist of the two quantities multiplying together. This result is new, and may be hopeful to find application in designing quantum adiabatic algorithm for problems beyond quantum search.

Polaron absorption in aligned conjugated polymer films: breakdown of adiabatic treatments and going beyond the conventional mid-gap state model.

This study provides the first experimental polarized intermolecular and intramolecular optical absorption components of field-induced polarons in regioregular poly(3-hexylthiophene-2,5-diyl), rr-P3HT, a polymer semiconductor. Highly aligned rr-P3HT thin films were prepared by a high temperature shear-alignment process that orients polymer backbones along the shearing direction. rr-P3HT in-plane molecular orientation was measured by electron diffraction, and out-of-plane orientation was measured through series of synchrotron X-ray scattering techniques. Then, with molecular orientation quantified, polarized charge modulation spectroscopy was used to probe mid-IR polaron absorption in the ℏω = 0.075 - 0.75 eV range and unambiguously assign intermolecular and intramolecular optical absorption components of hole polarons in rr-P3HT. This data represents the first experimental quantification of these polarized components and allowed long-standing theoretical predictions to be compared to experimental results. The experimental data is discrepant with predictions of polaron absorption based on an adiabatic framework that works under the Born-Oppenheimer approximation, but the data is entirely consistent with a more recent nonadiabatic treatment of absorption based on a modified Holstein Hamiltonian. This nonadiabatic treatment was used to show that both intermolecular and intramolecular polaron coherence break down at length scales significantly smaller than estimated structural coherence in either direction. This strongly suggests that polaron delocalization is fundamentally limited by energetic disorder in rr-P3HT.

Adiabatic hydrodynamization: A natural framework to find and describe prehydrodynamic attractors

The adiabatic hydrodynamization framework [1, 2] is a promising framework within which to describe and characterize pre-hydrodynamic attractors in a model-independent fashion. Using this framework, we define a procedure to identify a time-dependent change in coordinates which reveals a dynamical reduction in the number of active degrees of freedom. Applying this procedure to the kinetic theory of a Bjorken-expanding gas of gluons in the small angle elastic scattering limit, we are able to intuitively explain the selfsimilar evolution of the gluon distribution function long before the applicability of hydrodynamics, as well as the loss of memory of its initial condition.

Quantum cosmological backreactions. III. Deparametrized quantum cosmological perturbation theory

This is the third paper in a series of four in which we incorporate backreaction among the homogeneous as well as between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory using space adiabatic methods. Here, we consider a gauge-fixed version of cosmological perturbation theory which uses Gaussian dust as a material reference system. The observable matter content is a real-valued scalar field. We explore the sector of that theory which is purely homogeneous and isotropic with respect to the geometry degrees of freedom but which contains inhomogeneous perturbations up to second order of the scalar field. We explore the quantum field theoretical challenges of the space adiabatic framework in a cosmological model of the early universe which is technically still relatively simple. We compute the quantum backreaction effects from the inhomogeneous matter modes on the homogeneous geometry up to second order in the adiabatic parameter. It turns out that these contributions are not negligible.

An initial step toward a quantum annealing approach to the discrete logarithm problem

The discrete logarithm problem over a multiplicative group of integer modulo n is the key ingredient in the ElGamal encryption system. This problem has been proven to be tractable in polynomial time on a quantum computer by Shor's algorithm. This algorithm makes use of basic quantum gates, circuits, measurements and it has been experimented in the circuit-gate framework of quantum computing. On the other hand, the adiabatic framework of quantum computing with the quantum annealers such as the D-Wave machine that simulates the adiabatic process has become very popular, showing its potential for making a practical pathway to achieve quantum speedup. Furthermore, much progress has been reported recently on the tractability of the integer factoring problem, which is the other widely-used encryption method, on quantum annealers. In this context, it is important to explore the tractability of the discrete logarithm problem too using quantum annealers. In this work we present a first step made in this direction, by converting the discrete logarithm problem over a multiplicative group into the problem of minimizing a binary quadratic form, a standard problem format acceptable to a quantum annealer. Our formulation was tested for small-scale problem instances using the quantum-classical hybrid platform PyQUBO and we discuss the computational challenges and propose several potential improvements to the formulation.

Improved One-Shot Total Energies from the Linearized GW Density Matrix.

The linearized GW density matrix (γGW) is an efficient method to improve the static portion of the self-energy compared to that of ordinary perturbative GW while keeping the single-shot simplicity of the calculation. Previous work has shown that γGW gives an improved Fock operator and total energy components that approach the self-consistent GW quality. Here, we test γGW for dimer dissociation for the first time by studying N2, LiH, and Be2. We also calculate a set of self-consistent GW results in identical basis sets for a direct and consistent comparison. γGW approaches self-consistent GW total energies for a starting point based on a high amount of exact exchange. We also compare the accuracy of different total energy functionals, which differ when evaluated with a non-self-consistent density or density matrix. While the errors in total energies among different functionals and starting points are small, the individual energy components show noticeable errors when compared to reference data. The energy component errors of γGW are smaller than functionals of the density and we suggest that the linearized GW density matrix is a route to improving total energy evaluations in the adiabatic connection framework.

Quantum Zeno approach for molecular energies with maximum commuting initial Hamiltonians

We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.

Nonresonant Density of States Enhancement at Low Energies for Three or Four Neutrons.

The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated four-neutron ejection events observed experimentally in a nuclear reaction by Kisamori etal. [Phys. Rev. Lett. 116, 052501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.052501].

Configuration interaction singles with spin-orbit coupling: Constructing spin-adiabatic states and their analytical nuclear gradients.

For future use in modeling photoexcited dynamics and intersystem crossing, we calculate spin-adiabatic states and their analytical nuclear gradients within configuration interaction singles theory. These energies and forces should be immediately useful for surface hopping dynamics, which are natural within an adiabatic framework. The resulting code has been implemented within the Q-Chem software and preliminary results suggest that the additional cost of including spin-orbit coupling within the singles-singles block is not large.

Observation of the geometric phase effect in the H + HD → H2 + D reaction.

Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H2 + D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state-resolved differential cross sections in the forward scattering direction for H2 products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

Pinpointing the role of geometric phase

Chemical Physics During chemical reactions, electrons usually rearrange more quickly than nuclei. Thus, theorists often adopt an adiabatic framework that considers vibrational and rotational dynamics within single electronic states. Near the regime where two electronic states intersect, the dynamics get more complicated, and a geometric phase factor is introduced to maintain the simplifying power of the adiabatic treatment. Yuan et al. conducted precise experimental measurements that validate this approach. They studied the elementary H + HD reaction at energies just above the intersection of electronic states and observed angular oscillations in the product-state cross sections that are well reproduced by simulations that include the geometric phase. Science , this issue p. [1289][1] [1]: /lookup/doi/10.1126/science.aav1356

How intrinsic nuclear nonadiabaticity affects molecular structure, electronic density, and conformational stability: Insights from the multicomponent DFT calculations of Mu/H isotopologues

AbstractIn the present work, the formalism of the multicomponent density functional theory is extended to study the open‐shell muoniated radicals of nucleic acid bases adenine, guanine, cytosine, thymine and uracil beyond the adiabatic paradigm. The derived methodology is used to characterize the stationary structures of all conceivable muoniated adducts based on the ab initio nuclear‐electronic approach, which is a mixed intermediate non‐adiabatic/adiabatic framework. The energies, geometries, atomic charges and spin‐density distributions of the muoniated species are scrutinized against their hydrogenated congeners derived within the conventional adiabatic framework. The comparative analysis of the results determines the considerable impact of nuclear quantum effects on the molecular geometry, electronic density and conformational stability while underlining the fact that the extent of the geometrical and spin‐distribution variations upon muonium substitution could be significant and mass dependent.

OCS isomerization and dissociation kinetics from statistical models

In this work computational modeling of the isomerization reactions of the linear OCS, CSO, COS, and the cyclic Δ-OCS structures, on the ground state Potential Energy Surface (PES), is performed using Rice–Ramsperger–Kassel–Marcus (RRKM), Semiclassical Transition State Theory (SCTST), and the Master Equation (ME). Adiabatic dissociations of the sulfur atom from the OCS, $$\Delta $$ -OCS and COS structures are also studied with the Variational Transition State Theory (VTST). Intramolecular Vibrational Energy Redistributions (IVRs), calculated within the adiabatic approximation framework, appear to be faster than the corresponding reactions, justifying the use of statistical methods to study the kinetics of the reactions. From the microcanonical rate coefficients, we establish that the lifetimes of isomers $$\Delta $$ -OCS and COS are insufficient to complete one vibrational period of the corresponding molecules. The energy-specific branching ratios lead us to conclude that only 0.08 and 0.07% of molecules reacting from the most stable isomer OCS produce CSO and COS, respectively, at 180 kcal/mol (when all the reaction channels are open). This can be attributed to the dominance of the dissociation over the isomerizations. From the SCTST treatment, we find that coupling and tunneling are very important in this system, as deviations from the Arrhenius-type behavior in the reaction kinetics are considerable, particularly at low temperatures.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. II. 1D spectra for a dimer.

Vibrational-electronic resonance in photosynthetic pigment-protein complexes invalidates Förster's adiabatic framework for interpreting spectra and energy transfer, thus complicating determination of how the surrounding protein affects pigment properties. This paper considers the combined effects of vibrational-electronic resonance and inhomogeneous variations in the electronic excitation energies of pigments at different sites on absorption, emission, circular dichroism, and hole-burning spectra for a non-degenerate homodimer. The non-degenerate homodimer has identical pigments in different sites that generate differences in electronic energies, with parameters loosely based on bacteriochlorophyll a pigments in the Fenna-Matthews-Olson antenna protein. To explain the intensity borrowing, the excited state vibrational-electronic eigenvectors are discussed in terms of the vibrational basis localized on the individual pigments, as well as the correlated/anti-correlated vibrational basis delocalized over both pigments. Compared to those in the isolated pigment, vibrational satellites for the correlated vibration have the same frequency and precisely a factor of 2 intensity reduction through vibrational delocalization in both absorption and emission. Vibrational satellites for anti-correlated vibrations have their relaxed emission intensity reduced by over a factor 2 through vibrational and excitonic delocalization. In absorption, anti-correlated vibrational satellites borrow excitonic intensity but can be broadened away by the combination of vibronic resonance and site inhomogeneity; in parallel, their vibronically resonant excitonic partners are also broadened away. These considerations are consistent with photosynthetic antenna hole-burning spectra, where sharp vibrational and excitonic satellites are absent. Vibrational-excitonic resonance barely alters the inhomogeneously broadened linear absorption, emission, and circular dichroism spectra from those for a purely electronic excitonic coupling model. Energy transfer can leave excess energy behind as vibration on the electronic ground state of the donor, allowing vibrational relaxation on the donor's ground electronic state to make energy transfer permanent by removing excess energy from the excited electronic state of the dimer.

Dark matter spikes in the vicinity of Kerr black holes

The growth of a massive black hole will steepen the cold dark matter density at the center of a galaxy into a dense spike, enhancing the prospects for indirect detection. We study the impact of black hole spin on the density profile using the exact Kerr geometry of the black whole in a fully relativistic adiabatic growth framework. We find that, despite the transfer of angular momentum from the hole to the halo, rotation increases significantly the dark matter density close to the black hole. The gravitational effects are still dominated by the black hole within its influence radius, but the larger dark matter annihilation fluxes might be relevant for indirect detection estimates.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer.

Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence.

Electronic decoherence following photoionization: Full quantum-dynamical treatment of the influence of nuclear motion

Photoionization using attosecond pulses can lead to the formation of coherent superpositions of the electronic states of the parent ion. However, ultrafast electron ejection triggers not only electronic but also nuclear dynamics---leading to electronic decoherence, which is typically neglected on time scales up to tens of femtoseconds. We propose a full quantum-dynamical treatment of nuclear motion in an adiabatic framework, where nuclear wavepackets move on adiabatic potential energy surfaces expanded up to second order at the Franck-Condon point. We show that electronic decoherence is caused by the interplay of a large number of nuclear degrees of freedom and by the relative topology of the potential energy surfaces. Application to $\mathrm{H_2O}$, paraxylene, and phenylalanine shows that an initially coherent state evolves to an electronically mixed state within just a few femtoseconds. In these examples the fast vibrations involving hydrogen atoms do not affect electronic coherence at short times. Conversely, vibrational modes involving the whole molecular skeleton, which are slow in the ground electronic state, quickly destroy it upon photoionization.

Intra- and Intermolecular Singlet Fission in Covalently Linked Dimers

Electronic factors controlling singlet fission (SF) rates are investigated in four-chromophore model systems comprising two covalently linked dimers of tetracene. By using adiabatic framework and wave function analysis tools, we show that the lowest singlet multiexciton states are localized on the individual molecules. The intermolecular ME states, in which the triplet excitons reside on separate moieties, are higher in energy and are not accessible from the lowest singlet excitonic state. Although the electronic states from the excitonic/charge-resonance band are delocalized over the four chromophores, the calculations suggest that the essential electronic properties controlling the rates of SF depend largely on the electronic properties of the individual covalently linked chromophores, owing to the strong through-bond couplings.

The Interaction of an Eastward-Flowing Current and an Island: Sub- and Supercritical Flow

AbstractAn eastward-flowing current of a homogeneous fluid with velocity U, contained in a channel of width L, impinges on an island of width of O(L), and the resulting interaction and dynamics are studied for values of the supercriticality parameter, b = βL2/U, both larger and smaller than π2. The former case is subcritical with respect to Rossby waves, and the latter is supercritical. The nature of the flow field depends strongly on b, and in particular, the nature of the flow around the island and the proportion of the flow passing to the north or south of the island are sensitive to b and to the position of the island in the channel. The problem is studied analytically in a relatively simple, nonlinear quasigeostrophic and adiabatic framework and numerically with a shallow-water model that allows a qualitative extension of the results to the equator. Although the issues involved are motivated by the interaction of the Equatorial Undercurrent and the Galapagos Islands, the analysis presented here focuses on the fundamental issue of the distinctive nature of the flow as a function of Rossby wave criticality.

Adiabatic versus diabatic approach to multichannel Coulomb scattering for mutual neutralisation reaction [formula omitted

In this paper it is demonstrated that the split-potential driven Schrödinger approach to two-body Coulomb multichannel quantum scattering in a diabatic framework presented by us in a previous paper (Volkov et al., 2011) also can be formulated within an adiabatic framework. The new formulation of the theory is numerically realised using finite element discrete variable representation. The method is applied to a realistic model of the fundamental mutual neutralisation reaction H++H-→H2∗→H(1)+H(n) described in terms of the seven lowest 1Σg+ electronic states of the H2 molecule. The obtained cross sections are in good agreement with other methods applied to the same model.