arXiv subjects

Ove Christiansen

Publications and source records attributed to Ove Christiansen.

16 recordsLinked to original sources

arXiv2026

Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, $N$, and low-order polynomial scaling with dimensionality, $D$. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. We demonstrate the scalability of the matrix-vector product by running benchmarks with billions of data points and thousands of dimensions. Full GPR calculations, including hyperparameter optimization, are completed in a matter of hours for $N = 447 265$ and $D = 24$. We demonstrate that our CUTS-GPR enables Bayesian modeling of high-dimensional potential energy surfaces - a longstanding challenge in computational chemistry.

cs.LG↗

arXiv2025

Fault-tolerant quantum computations of vibrational wave functions

Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively unexplored field in quantum computing. In this work, we present different algorithms for efficient encodings of vibrational Hamiltonians using qubitization. Specifically, we investigate different encoding representations, high order tensor decomposition to obtain low rank approximations for the vibrational Hamiltonian, rectilinear and polyspherical coordinate systems, parallelization and grouping algorithms. To investigate the performance of the different methods, we perform benchmark computations for both small and large molecules with more than one hundred vibrational modes.

quant-ph↗

arXiv2025

Vibrational ADAPT-VQE: Critical points leads to problematic convergence

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remain a relatively unexplored field. In this work, we develop a vibrational ADAPT-VQE (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT- VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators which may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

quant-ph↗

arXiv2024

Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structure of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.

quant-ph↗

arXiv2024

A bivariational, stable and convergent hierarchy for time-dependent coupled cluster with adaptive basis sets

We propose a new formulation of time-dependent coupled cluster with adaptive basis functions and division of the one-particle space into active and secondary subspaces. The formalism is fully bivariational in the sense of a real-valued time-dependent bivariational principle and converges to the complete-active-space solution, a property that is obtained by the use of biorthogonal basis functions. A key and distinguishing feature of the theory is that the active bra and ket functions span the same space by construction. This ensures numerical stability and is achieved by employing a split unitary/non-unitary basis set transformation: The unitary part changes the active space itself, while the non-unitary part transforms the active basis. The formulation covers vibrational as well as electron dynamics. Detailed equations of motion are derived and implemented in the context of vibrational dynamics, and the numerical behavior is studied and compared to related methods.

physics.chem-ph↗

arXiv2024

Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning

Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent in current quantum processing units (QPUs). This challenge is also decisive in the context of quantum-classical hybrid schemes employing variational quantum eigensolvers (VQEs) that have attracted significant interest in recent years. In this work, we present a novel method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations, focusing on VQEs. Our approach, grounded in probabilistic machine learning, exploits a custom prior based on the VQE ansatz to capture the underlying correlations between VQE outputs for different variational parameters, thereby enhancing both accuracy and efficiency. We demonstrate the effectiveness of our method on a 2-site Anderson impurity model and a 8-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit, showcasing substantial improvements in the accuracy of VQE outputs while reducing the number of direct QPU energy evaluations. This work contributes to the ongoing efforts in quantum error mitigation and optimization, bringing us a step closer to realizing the potential of quantum computing in quantum matter simulations.

quant-ph↗

arXiv2023

Active Learning approach to simulations of Strongly Correlated Matter with the Ghost Gutzwiller Approximation

Quantum embedding (QE) methods such as the Ghost Gutzwiller Approximation (gGA) offer a powerful approach to simulating strongly-correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly-correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly-correlated materials.

cond-mat.str-el↗

arXiv2023

Time-dependent coupled cluster with orthogonal adaptive basis functions: General formalism and application to the vibrational problem

We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster ansatz. The equations are related to the biorthogonal case in a transparent way, and similarities and differences are analyzed. We show that the amplitude equations are identical in the orthogonal and biorthogonal formalisms, while the linear equations that determined the basis set time evolution differ by symmetrization. Applying the orthogonal framework to the nuclear dynamics problem, we introduce and implement the orthogonal time-dependent modal vibrational coupled cluster (oTDMVCC) method and benchmark it against exact reference results for four triatomic molecules as well as a 5D trans-bithiophene model. We confirm numerically that the biorthogonal TDMVCC hierarchy converges to the exact solution, while oTDMVCC does not. The differences between TDMVCC and oTDMVCC are found to be small for three of the five cases, but we also identify one case where the formal deficiency of the oTDMVCC approach results in clear and visible errors relative to the exact result. For the remaining example, oTDMVCC exhibits rather modest but visible errors.

physics.chem-ph↗

arXiv2023

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: full and hybrid TDMVCC[2]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper we report an efficient implementation of TDMVCC covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and ii) the use of a single function as active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH approach which can obtain an even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] are illustrated for polyaromatic hydrocarbons (PAHs) with up to 264 modes. Finally, computations on the internal vibrational redistribution on benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

physics.chem-ph↗

arXiv2023

General exponential basis set parametrization: Application to time-dependent bivariational wave functions

We present equations of motion (EOMs) for general time-dependent wave functions with exponentially parametrized biorthogonal basis sets. The equations are fully bivariational in the sense of the time-dependent bivariational principle (TDBVP) and offer an alternative, constraint free formulation of adaptive basis sets for bivariational wave functions. We simplify the highly non-linear basis set equations using Lie algebraic techniques and show that the computationally intensive parts of the theory are in fact identical to those that arise with linearly parametrized basis sets. Our approach thus offers easy implementation on top of existing code with minimal computational overhead in the context of both nuclear dynamics and time-dependent electronic structure. Computationally tractable working equations are provided for single and double exponential parametrizations of the basis set evolution. The EOMs are generally applicable for any value of the basis set parameters, unlike the approach of transforming the parameters to zero at each evaluation of the EOMs. We show that the basis set equations contain a well-defined set of singularities, which are identified and removed by a simple scheme. The exponential basis set equations are implemented in conjunction with time-dependent vibrational coupled cluster with time-dependent modals (TDMVCC) and we investigate the propagation properties in terms of the average integrator step size. For the systems we test, the exponentially parametrized basis sets yield slightly larger step sizes compared to linearly parametrized basis set.

physics.chem-ph↗

arXiv2023

Gaussian Process Regression Adaptive Density-Guided Approach: Towards Calculations of Potential Energy Surfaces for Larger Molecules

We present a new program implementation of the gaussian process regression adaptive density-guided approach [J. Chem. Phys. 153 (2020) 064105] in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach towards calculations of larger molecular systems than those accessible previously and maintain the very high accuracy of constructed potential energy surfaces. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80 % of single point calculations could be avoided introducing a root mean square deviation in fundamental excitations of about 3 cm$^{-1}$. A much higher accuracy with errors below 1 cm$^{-1}$ could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68 %. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly-accurate vibrational spectra simulations.

physics.chem-ph↗

arXiv2021

Quantum-embedding description of the Anderson lattice model with the ghost Gutzwiller Approximation

We present benchmark calculations of the Anderson lattice model based on the recently-developed "ghost Gutzwiller approximation". Our analysis shows that, in some parameters regimes, the predictions of the standard Gutzwiller approximation can be incorrect by orders of magnitude for this model. We show that this is caused by the inability of this method to describe simultaneously the Mott physics and the hybridization between correlated and itinerant degrees of freedom (whose interplay often governs the metal-insulator transition in real materials). Finally, we show that the ghost Gutzwiller approximation solves this problem, providing us with results in remarkable agreement with dynamical mean field theory throughout the entire phase diagram, while being much less computationally demanding. We provide an analytical explanation of these findings and discuss their implications within the context of ab-initio computation of strongly-correlated matter.

cond-mat.str-el↗

arXiv2020

Vibrationally Resolved Coupled Cluster X-Ray Absorption Spectra from Vibrational Configuration Interaction Anharmonic Calculations

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the Adaptive Density-Guided Approach (ADGA) scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules

physics.chem-ph↗

arXiv2020

Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we design a computational framework combining quantum-embedding (QE) methods with machine learning. This allows us to bypass altogether the most computationally-expensive components of QE algorithms, making their overall cost comparable to bare Density Functional Theory (DFT). We perform benchmark calculations of a series of actinide systems, where our method describes accurately the correlation effects, reducing by orders of magnitude the computational cost. We argue that, by producing a larger-scale set of training data, it will be possible to apply our method to systems with arbitrary stoichiometries and crystal structures, paving the way to virtually infinite applications in condensed matter physics, chemistry and materials science.

cond-mat.str-el↗

arXiv2020

Adaptive Density-Guided Approach to Double Incremental Potential Energy Surface Construction

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an incremental expansion for potential energy surfaces, known as n-mode expansion, an incremental many-body representation of the electronic energy, and an efficient vibrational density-guided approach to automated determination of grid dimensions and granularity. The reliability of the method is validated calculating potential energy surfaces and obtaining fundamental excitation energies for three moderate-size chain-like molecular systems. The results are compared to other approaches, which utilize static grid construction for supersystem and fragmentation calculation setups. The use of our methodology leads to considerable computational savings for potential energy surface construction and a major reduction in the number of required single point calculations can be achieved, while maintaining a high level of accuracy in the resulting potential energy surfaces. Additional investigations indicate that our method can be applied to covalently bound and strongly interacting molecular systems, even though these cases are known as being very unfavorable for fragmentation schemes. We therefore conclude that the presented methodology is a robust and flexible approach to potential energy surface construction, which introduces considerable computational savings without compromising the accuracy of vibrational spectra calculations.

physics.chem-ph↗

arXiv2016

Linear-scaling generation of potential energy surfaces using a double incremental expansion

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.

physics.chem-ph↗