arXiv subjects

Bruno Senjean

Publications and source records attributed to Bruno Senjean.

33 records · Page 2Linked to original sources

arXiv2021

Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model

Variational quantum algorithms (VQA) are considered as some of the most promising methods to determine the properties of complex strongly correlated quantum many-body systems, especially from the perspective of devices available in the near term. In this context, the development of efficient quantum circuit ansatze to encode a many-body wavefunction is one of the keys for the success of a VQA. Great efforts have been invested to study the potential of current quantum devices to encode the eigenstates of fermionic systems, but little is known about the encoding of bosonic systems. In this work, we investigate the encoding of the ground state of the (simple but rich) attractive Bose-Hubbard model using a Continuous-Variable (CV) photonic-based quantum circuit. We introduce two different ansatz architectures and demonstrate that the proposed continuous variable quantum circuits can efficiently encode (with a fidelity higher than 99%) the strongly correlated many-boson wavefunction with just a few layers, in all many-body regimes and for different number of bosons and initial states. Beyond the study of the suitability of the ansatz to approximate the ground states of many-boson systems, we also perform initial evaluations of the use of the ansatz in a variational quantum eigensolver algorithm to find it through energy minimization. To this end we also introduce a scheme to measure the Hamiltonian energy in an experimental system, and study the effect of sampling noise.

quant-ph↗

arXiv2021

Orbital transformations to reduce the 1-norm of the electronic structure Hamiltonian for quantum computing applications

Reducing the complexity of quantum algorithms to treat quantum chemistry problems is essential to demonstrate an eventual quantum advantage of Noisy-Intermediate Scale Quantum (NISQ) devices over their classical counterpart. Significant improvements have been made recently to simulate the time-evolution operator $U(t) = e^{i\mathcal{\hat{H}}t}$ where $\mathcal{\hat{H}}$ is the electronic structure Hamiltonian, or to simulate $\mathcal{\hat{H}}$ directly (when written as a linear combination of unitaries) by using block encoding or "qubitization" techniques. A fundamental measure quantifying the practical implementation complexity of these quantum algorithms is the so-called "1-norm" of the qubit-representation of the Hamiltonian, which can be reduced by writing the Hamiltonian in factorized or tensor-hypercontracted forms for instance. In this work, we investigate the effect of classical pre-optimization of the electronic structure Hamiltonian representation, via single-particle basis transformation, on the 1-norm. Specifically, we employ several localization schemes and benchmark the 1-norm of several systems of different sizes (number of atoms and active space sizes). We also derive a new formula for the 1-norm as a function of the electronic integrals, and use this quantity as a cost function for an orbital-optimization scheme that improves over localization schemes. This paper gives more insights about the importance of the 1-norm in quantum computing for quantum chemistry, and provides simple ways of decreasing its value to reduce the complexity of quantum algorithms.

quant-ph↗

arXiv2021

Generalization of intrinsic orbitals to Kramers-paired quaternion spinors, molecular fragments and valence virtual spinors

Localization of molecular orbitals finds its importance in the representation of chemical bonding (and anti-bonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11, 4834-4843] to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only. By performing a singular value decomposition, we show how localized valence virtual orbitals can be expressed in this intrinsic minimal basis. We demonstrate our method on systems of increasing complexity, starting from simple cases such as benzene, acrylic-acid and ferrocene molecules, and then demonstrating the use of molecular fragments and inclusion of relativistic effects for complexes containing heavy elements such as tellurium, iridium and astatine. The aforementioned scheme is implemented into a standalone program interfaced with several different quantum chemistry packages.

physics.chem-ph↗

arXiv2021

A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states

In the Noisy Intermediate-Scale Quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the "killer application" for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While physically motivated, this approximation can severely impact the description of these complicated features. A perfect example is that of conical intersections (i.e. a singular point of degeneracy between electronic states), which are of primary importance to understand many prominent reactions. Designing active spaces so that the improved accuracy from a quantum computer is not rendered useless is key to finding useful applications of these promising devices within the field of chemistry. To answer this issue, we introduce a NISQ-friendly method called "State-Averaged Orbital-Optimized Variational Quantum Eigensolver" (SA-OO-VQE) which combines two algorithms: (1) a state-averaged orbital-optimizer, and (2) a state-averaged VQE. To demonstrate the success of the method, we classically simulate it on a minimal Schiff base model (namely the formaldimine molecule CH2NH) relevant also for the photoisomerization in rhodopsin -- a crucial step in the process of vision mediated by the presence of a conical intersection. We show that merging both algorithms fulfil the necessary condition to describe the molecule's conical intersection, i.e. the ability to treat degenerate (or quasi-degenerate) states on the same footing.

quant-ph↗

arXiv2020

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems

Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the excitation energies. In the present article, we discuss the construction of first-rung (i.e., local) weight-dependent exchange-correlation density-functional approximations for two-electron atomic and molecular systems (He and H$_2$) specifically designed for the computation of double excitations within GOK-DFT. In the spirit of optimally-tuned range-separated hybrid functionals, a two-step system-dependent procedure is proposed to obtain accurate energies associated with double excitations.

physics.chem-ph↗

arXiv2020

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for 1-, 2- and 4-component relativistic molecular calculations at the level of Hartree--Fock, Kohn--Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, coupled cluster and electron propagator theory. At the self-consistent-field level a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding, and frozen density embedding models. DIRAC was one of the earliest codes for relativistic molecular calculations and remains a reference in its field.

physics.chem-ph↗

arXiv2020

N-centered ensemble density-functional theory for open systems

Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513 (2018)] are presented. Unlike the original formulation of the theory, these variants allow for the description of systems with a fractional electron number. While conventional DFT for open systems uses only the true electron density as basic variable, left/right N-centered ensemble DFT relies instead on (i) a fictitious ensemble density that integrates to a central (integral) number N of electrons, and (ii) a grand canonical ensemble weight $α$ which is equal to the deviation of the true electron number from N. Within such a formalism, the infamous derivative discontinuity that appears when crossing an integral number of electrons is described exactly through the dependence in $α$ of the left and right N-centered ensemble Hartree-exchange-correlation density functionals. Incorporating N-centered ensembles into existing density-functional embedding theories is expected to pave the way towards the in-principle-exact description of an open fragment by means of a pure-state N-electron many-body wavefunction. Work is currently in progress in this direction

cond-mat.str-el↗

arXiv2019

Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory

Site-occupation embedding theory (SOET) is an in-principle-exact multi-determinantal extension of density-functional theory for model Hamiltonians. Various extensions of recent developments in SOET [Senjean et al., Phys. Rev. B 97, 235105 (2018)] are explored in this work. An important step forward is the generalization of the theory to multiple impurity sites. We also propose a new single-impurity density-functional approximation (DFA) where the density-functional impurity correlation energy of the two-level (2L) Hubbard system is combined with the Bethe ansatz local density approximation (BALDA) to the full correlation energy of the (infinite) Hubbard model. In order to test the new DFAs, the impurity-interacting wavefunction has been computed self-consistently with the density matrix renormalization group method (DMRG). Double occupation and per-site energy expressions have been derived and implemented in the one-dimensional case. A detailed analysis of the results is presented, with a particular focus on the errors induced either by the energy functionals solely or by the self-consistently converged densities. Among all the DFAs (including those previously proposed), the combined 2L-BALDA is the one that performs the best in all correlation and density regimes. Finally, extensions in new directions, like a partition-DFT-type reformulation of SOET, a projection-based SOET approach, or the combination of SOET with Green functions, are briefly discussed as a perspective.

cond-mat.str-el↗

arXiv2019

Projected site-occupation embedding theory

Site-occupation embedding theory (SOET) [B. Senjean et al., Phys. Rev. B 97, 235105 (2018)] is an in-principle exact embedding method combining wavefunction theory and density functional theory that gave promising results when applied to the one-dimensional Hubbard model. Despite its overall good performance, SOET faces a computational cost problem as its auxiliary impurity-interacting system remains the size of the full system (which is problematic as the computational cost increases exponentially with system size). In this work, this issue is circumvented by employing the Schmidt decomposition, thus leading to a drastic reduction of the computational cost while retaining the same accuracy. We show that this projected version of SOET (P-SOET) is competitive with other embedding techniques such as density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. In contrast to the latter, density functional contributions come naturally into play in P-SOET's framework without any additional computational cost or double counting effect. As an important result, the density-driven Mott-Hubbard transition (which is displayed by multiple impurity sites in DMET or in dynamical mean-field theory) is well described, for the first time, with a single impurity site.

cond-mat.str-el↗

arXiv2018

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference, we show that the two problems can be made formally identical by introducing a universal and canonical ensemble weight dependent exchange-correlation (xc) density functional. The weight dependence of the xc energy turns out to be the key ingredient for describing the infamous derivative discontinuity and represents a new path for its approximation.

physics.chem-ph↗

arXiv2018

Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer

Gross-Oliveira-Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excited-state densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre-Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.

cond-mat.str-el↗

arXiv2018

Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations

Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wavefunction has been performed with the density matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

cond-mat.str-el↗

arXiv2016

Local density approximation in site-occupation embedding theory

Site-occupation embedding theory (SOET) is a density-functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially-interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform 8-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.

cond-mat.str-el↗

arXiv2015

Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory

The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical mu=0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly-excited 2^1Sigma+g state in the stretched H2 molecule. Three-state ensemble calculations in H2 also show that ELIM does not necessarily improves relative excitation energies, even though individual excitation energies are more accurate after extrapolation. Finally, an alternative decomposition of the short-range ensemble exchange-correlation energy is proposed in order to correct for ghost-interaction errors in multideterminant range-separated ensemble density-functional theory calculations. The implementation and calibration of such a scheme is currently in progress.

physics.chem-ph↗

arXiv2015

Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states

Gross-Oliveira-Kohn density functional theory (GOK-DFT) for ensembles is in principle very attractive, but has been hard to use in practice. A novel, practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The new model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly-interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) can be rationalized and that it effectively introduces weight dependence effects. As proof of principle, LIM has been applied to He, Be, H$_2$ in both equilibrium and stretched geometries as well as the stretched HeH$^+$ molecule. Very promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semi-local functionals. Even at the Kohn--Sham ensemble DFT level, that is recovered when the range-separation parameter is set to zero, LIM performs better than standard time-dependent DFT.

physics.chem-ph↗