arXiv subjects

Artur F. Izmaylov

Publications and source records attributed to Artur F. Izmaylov.

At least 73 records · Page 4Linked to original sources

arXiv2019

Quantum chemistry on quantum annealers

Quantum chemistry calculations for small molecules on quantum hardware have been demonstrated to date only on universal-gate quantum computers, not quantum annealers. The latter devices are limited to finding the lowest eigenstate of the Ising Hamiltonian whereas the electronic Hamiltonian could not be mapped to the Ising form without exponential growth of the Ising Hamiltonian with the size of the system [J. Phys. Chem. B 122, 3384 (2018)]. Here we propose a novel mixed discrete-continuous optimization algorithm, which finds the lowest eigenstate of the qubit coupled cluster (QCC) method using a quantum annealer for solving a discrete part of the problem. The QCC method is a potentially exact approach for constructing the electronic wave function in the qubit space. Therefore, our methodology allows for systematically improvable quantum chemistry calculations using quantum annealears. We illustrate capabilities of our approach by calculating QCC ground electronic states for the LiH, H$_2$O, and C$_6$H$_6$ molecules. C$_6$H$_6$ calculations involve 36 qubits and are the largest quantum chemistry calculations made on a quantum annealer (the D-Wave 2000Q system) to date. Our findings opens up a new perspective for use quantum annealers in high-throughput material discovery.

physics.chem-ph↗

arXiv2018

Qubit coupled-cluster method: A systematic approach to quantum chemistry on a quantum computer

A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry problems on a quantum computer. Although being exact in the limit of including all possible coupled-cluster excitations, practically, the accuracy of this approach depends on how many and what kind of terms are included in the wavefunction parametrization. Another difficulty of UCC is a growth of the number of simultaneously entangled qubits even at the fixed fermionic excitation rank. Not all quantum computing architectures can cope with this growth. To address both problems we introduce a qubit coupled-cluster (QCC) method that starts directly in the qubit space and uses energy response estimates for ranking the importance of individual entanglers for the variational energy minimization. Also, we provide an exact factorization of a unitary rotation of more than two qubits to a product of two-qubit unitary rotations. Thus, the QCC method with the factorization technique can be limited to only two-qubit entanglement gates and allows for very efficient use of quantum resources in terms of the number of coupled-cluster operators. The method performance is illustrated by calculating ground-state potential energy curves of H$_2$ and LiH molecules with chemical accuracy, $\le 1$ kcal/mol.

quant-ph↗

arXiv2018

On the Breakdown of the Ehrenfest Method for Molecular Dynamics on Surfaces

Due to a continuum of electronic states present in periodic systems, the description of molecular dynamics on surfaces poses a serious computational challenge. One of the most used families of approaches in these settings are friction theories, which are based on the Ehrenfest (EH) approach. Yet, a mean-field treatment of electronic degrees of freedom in the EH method makes this approach inaccurate in some cases. Our aim is to clarify when EH breaks down for molecular dynamics on surfaces. Answering this question provides limits of applicability for more approximate friction theories derived from EH. We assess the EH method on one-dimensional, numerically exactly solvable models with a large but finite number of electronic states. Using the Landau-Zener formula and the Massey parameter, an expression that determines when EH breaks down is deduced.

physics.chem-ph↗

arXiv2018

Exploring vibrational ladder climbing in vibronic coupling models: Toward experimental observation of a geometric phase signature of a conical intersection

Conical intersections (CIs) have been widely studied using spectroscopic techniques. However, CIs have mainly been identified by rapid internal conversion transitions that take place after the photoexcitation. Such identifications cannot distinguish various types of intersections as well as to separate the actual intersection from an avoided crossing. In this paper, we investigate how ultrafast IR laser pulses can be utilized to stimulate nuclear dynamics revealing geometric phase features associated with CIs. We consider two low-dimensional nonadiabatic models to obtain optimal two- and three-pulse laser sequences for stimulating nuclear dynamics necessary for the CI identification. Our results provide insights on designing non-linear spectroscopic schemes for subsequent probes of the nuclear wavepackets by ultrafast electron diffraction techniques to unambiguously detect CIs in molecules.

physics.chem-ph↗

arXiv2018

Constrained variational quantum eigensolver: Quantum computer search engine in the Fock space

Variational quantum eigensolver (VQE) is an efficient computational method promising chemical accuracy in electronic structure calculations on a universal-gate quantum computer. However, such a simple task as computing the electronic energy of a hydrogen molecular cation, H$_2^+$, is not possible for a general VQE protocol because the calculation will invariably collapse to a lower energy of the corresponding neutral form, H$_2$. The origin of the problem is that VQE effectively performs an unconstrained energy optimization in the Fock space of the original electronic problem. We show how this can be avoided by introducing necessary constraints directing VQE to the electronic state of interest. The proposed constrained VQE can find an electronic state with a certain number of electrons, spin, or any other property. The new algorithm does not require any additional quantum resources. We demonstrate performance of the constrained VQE by simulating various states of H$_2$ and H$_2$O on Rigetti Computing Inc's 19Q-Acorn quantum processor.

physics.chem-ph↗

arXiv2018

Relation between fermionic and qubit mean fields in the electronic structure problem

For quantum computing applications, the electronic Hamiltonian for the electronic structure problem needs to be unitarily transformed to a qubit form. We found that mean-field procedures on the original electronic Hamiltonian and on its transformed qubit counterpart can give different results. We establish conditions of when fermionic and qubit mean fields provide the same or different energies. In cases when the fermionic mean-field (Hartree-Fock) approach provides an accurate description (electronic correlation effects are small), the choice of molecular orbitals for the electron Hamiltonian representation becomes the determining factor in whether the qubit mean-field energy will be equal to or higher than that of the fermionic counterpart. In strongly correlated cases, the qubit mean-field approach has a higher chance to undergo symmetry breaking and lower its energy below the fermionic counterpart.

physics.chem-ph↗

arXiv2018

Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians

We review techniques for simulating fully quantum nonadiabatic dynamics using the frozen-width moving Gaussian basis functions to represent the nuclear wavefunction. A choice of these basis functions is primarily motivated by the idea of the on-the-fly dynamics that will involve electronic structure calculations done locally in the vicinity of each Gaussian center and thus avoiding the "curse of dimensionality" appearing in large systems. For quantum dynamics involving multiple electronic states there are several aspects that need to be addressed. First, the choice of the electronic state representation is one of most defining in terms of formulation of resulting equations of motion. We will discuss pros and cons of the standard adiabatic and diabatic representations as well as the relatively new moving crude adiabatic representation. Second, if the number of electronic states can be fixed throughout the dynamics, the situation is different for the number of Gaussians needed for an accurate expansion of the total wavefunction. The latter increases its complexity along the course of the dynamics and a protocol extending the number of Gaussians is needed. We will consider two common approaches for the extension: 1) spawning and 2) cloning. Third, equations of motion for individual Gaussians can be chosen in different ways, implications for the energy conservation related to these ways will be discussed. Finally, to extend the success of moving basis approaches to quantum dynamics of open systems we will consider the Non-stochastic Open System Schrödinger Equation (NOSSE).

physics.chem-ph↗

arXiv2018

Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure

A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is elimination of any global or local model representation of electronic potential energy surfaces, instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.

physics.chem-ph↗

arXiv2017

Topological origins of bound states in the continuum for systems with conical intersections

Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original two-dimensional two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove the GP within a two-state problem. Using the stabilization graph technique we shown that the GP is crucial for emergence of BSCs.

physics.chem-ph↗

arXiv2017

Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study

We investigate geometric phase (GP) effects in nonadiabatic transitions through a conical intersection (CI) in an N-dimensional linear vibronic coupling (ND-LVC) model. This model allows for the coordinate transformation encompassing all nonadiabatic effects within a two-dimensional (2D) subsystem while the other N-2 dimensions form a system of uncoupled harmonic oscillators identical for both electronic states and coupled bi-linearly with the subsystem coordinates. The 2D subsystem governs ultra-fast nonadiabatic dynamics through the CI and provides a convenient model for studying GP effects. Parameters of the original ND-LVC model define the Hamiltonian of the transformed 2D subsystem and thus influence GP effects directly. Our analysis reveals what values of ND-LVC parameters can introduce symmetry breaking in the 2D subsystem that diminishes GP effects.

physics.chem-ph↗

arXiv2017

Quantum Nonadiabatic Cloning of Entangled Coherent States

We propose a systematic approach to the basis set extension for nonadiabatic dynamics of entangled combination of nuclear coherent states (CSs) evolving according to the time-dependent variational principle (TDVP). TDVP provides a rigorous framework for fully quantum nonadiabatic dynamics of closed systems, however, quality of results strongly depends on available basis functions. Starting with a single nuclear CS replicated vertically on all electronic states, our approach clones this function when replicas of the CS on different electronic states experience increasingly different forces. Created clones move away from each other (decohere) extending the basis set. To determine a moment for cloning we introduce generalized forces based on derivatives that maximally contribute to a variation of the total quantum action and thus account for entanglement of all basis functions.

physics.chem-ph↗

arXiv2016

Mixed quantum-classical dynamics using collective electronic variables: A better alternative to electronic friction theories

An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely-spaced electronic states. We propose a mixed quantum-classical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic block-diagonalization applied to the time-dependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with the Ehrenfest approach and with a full-memory electronic friction model on a one-dimensional "adatom + atomic chain" model. Our simulations demonstrate that collective-mode dynamics with only few (2-3) electronic variables is robust and can describe a variety of situations: from a chemisorbed atom on an insulator to an atom on a metallic surface. Our molecular model also reveals that the friction approach is prone to unpredictable and catastrophic failures.

physics.chem-ph↗

arXiv2016

Topologically correct quantum nonadiabatic formalism for on-the-fly dynamics

On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical intersections introduce non-trivial geometric or Berry phases which require a special treatment for adequate modelling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on the nuclear coordinates. The second approach uses adiabatic electronic functions obtained only at the centres of moving localized nuclear basis functions (e.g. frozen-width Gaussians). Unless a gauge transformation is used to enforce single-valued boundary conditions, the first approach fails to capture the geometric phase. In contrast, the second approach accounts for the geometric phase naturally because of the absence of the global nuclear coordinate dependence in the electronic functions.

physics.chem-ph↗

arXiv2016

Illustrating Electric Conductivity Using the Particle-in-a-Box Model: Quantum Superposition is the Key

Most of the textbooks explaining electric conductivity in the context of quantum mechanics provide either incomplete or semi-classical explanations that are not connected with the elementary concepts of quantum mechanics. We illustrate the conduction phenomena using the simplest model system in quantum dynamics, a particle in a box (PIB). To induce the particle dynamics, a linear potential tilting the bottom of the box is introduced, which is equivalent to imposing a constant electric field for a charged particle. Although the PIB model represents a closed system that cannot have a flow of electrons through the system, we consider the oscillatory dynamics of the particle probability density as the analogue of the electric current. Relating the amplitude and other parameters of the particle oscillatory dynamics with the gap between the ground and excited states of the PIB model allows us to demonstrate one of the most basic dependencies of electric conductivity on the valence-conduction band gap of the material.

physics.gen-ph↗

arXiv2016

Localized operator partitioning method for electronic excitation energies in the time-dependent density functional formalism

We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1-naphthyl)-methyl)-anthracene and 4-((2-naphthyl)-methyl)-benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.

physics.chem-ph↗

arXiv2016

A diabatic definition of geometric phase effects

Electronic wave-functions in the adiabatic representation acquire nontrivial geometric phases (GPs) when corresponding potential energy surfaces undergo conical intersection (CI). These GPs have profound effects on the nuclear quantum dynamics and cannot be eliminated in the adiabatic representation without changing the physics of the system. To define dynamical effects arising from the GP presence the nuclear quantum dynamics of the CI containing system is compared with that of the system with artificially removed GP. We explore a new construction of the system with removed GP via a modification of the diabatic representation for the original CI containing system. Using an absolute value function of diabatic couplings we remove the GP while preserving adiabatic potential energy surfaces and CI. We assess GP effects in dynamics of a two-dimensional linear vibronic coupling model both for ground and excited state dynamics. Results are compared with those obtained with a conventional removal of the GP by ignoring double-valued boundary conditions of the real electronic wave-functions. Interestingly, GP effects appear similar in two approaches only for the low energy dynamics. In contrast with the conventional approach, a new approach does not have substantial GP effects in the ultra-fast excited state dynamics.

physics.chem-ph↗

arXiv2016

Entanglement in the Born-Oppenheimer Approximation

The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the degree of electron-nuclear entanglement is found to be uncorrelated with the degree of validity of the BO approximation. This is because while the degree of entanglement of BO states is determined by their deviation from the corresponding states in the crude BO approximation, the accuracy of the BO approximation is dictated, instead, by the deviation of the BO states from the exact electron-nuclear states. In fact, in the context of a minimal avoided crossing model, extreme cases are identified where an adequate BO state is seen to be maximally entangled, and where the BO approximation fails but the associated BO state remains approximately unentangled. Further, the BO states are found to not preserve the entanglement properties of the exact electron-nuclear eigenstates, and to be completely unentangled only in the limit in which the BO approximation becomes exact.

quant-ph↗

arXiv2016

On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods

The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabatic dynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabatic dynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: 1) nuclei have kinetic energy lower than DBOC and 2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.

physics.chem-ph↗