Excited‐State Calculations with Quantum Monte Carlo

Feldt, Jonas; Filippi, Claudia

doi:10.1002/9781119417774.ch8

Cited by 14 publications

(11 citation statements)

References 92 publications

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“…Another way to extend the crystal spectral warping method would be through using methods other than semi-local/hybrid TDDFT for the two levels of calculation. In particular, going beyond hybrid TDDFT could allow phenomena such as excitons to be included; such methods could include the Bethe–Salpeter equation, quantum Monte Carlo, or even (multi-reference) coupled cluster theory . However, there are three considerations regarding which methods could be picked.…”

Section: Potential Future Extensionsmentioning

confidence: 99%

Accurate and Efficient Computation of Optical Absorption Spectra of Molecular Crystals: The Case of the Polymorphs of ROY

Prentice

Mostofi

2021

J. Chem. Theory Comput.

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When calculating the optical absorption spectra of molecular crystals from first principles, the influence of the crystalline environment on the excitations is of significant importance. For such systems, however, methods to describe the excitations accurately can be computationally prohibitive due to the relatively large system sizes involved. In this work, we demonstrate a method that allows optical absorption spectra to be computed both efficiently and at high accuracy. Our approach is based on the spectral warping method successfully applied to molecules in solvent. It involves calculating the absorption spectrum of a supercell of the full molecular crystal using semi-local time-dependent density functional theory (TDDFT), before warping the spectrum using a transformation derived from smallerscale semi-local and hybrid TDDFT calculations on isolated dimers. We demonstrate the power of this method on three polymorphs of the well-known color polymorphic compound ROY and find that it outperforms both small-scale hybrid TDDFT dimer calculations and large-scale semi-local TDDFT supercell calculations, when compared to the experiment.

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Section: Potential Future Extensionsmentioning

confidence: 99%

Accurate and Efficient Computation of Optical Absorption Spectra of Molecular Crystals: The Case of the Polymorphs of ROY

Prentice

Mostofi

2021

J. Chem. Theory Comput.

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“…Recently, it has been demonstrated that the scaling of computing a multideterminant expansion and optimizing can also be strongly reduced. − This is done using the determinant Lemma which allows a Slater determinant to be updated efficiently when only a few columns are modified. QMC has been used extensively for the description of materials including excited states …”

Section: Introductionmentioning

confidence: 99%

Stochastic Effective Core Potentials, toward Efficient Quantum Monte Carlo Simulations of Molecules with Large Atomic Numbers

Feldt

Assaraf

2021

J. Chem. Theory Comput.

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We propose a Monte Carlo method which exploits that core regions are physically independent in a molecule to almost remove their contribution to the numerical cost. The method is tantamount to computing an effective core potential on the fly, by efficiently subsampling the core regions with independent sidewalks. The removal of fluctuations in the core region enables also the dynamic in the valence region to be accelerated using a process with two time steps. As a function of the total number of electrons N the numerical overhead O(N) is negligible in comparison to the overall scaling O(N 3 ) (due to the evaluation of determinants). Tests are presented on atoms, alkane chains, and clusters of silicons. We report a transferability of the parameters of the method from atoms to molecules, enabling a calibration using only single atoms. These tests display a gain in numerical efficiency between one and two orders of magnitude for large N.

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“…On the classical computing side, state-of-the-art methods such as quantum Monte-Carlo (QMC) simulations have proven to be effective [20][21][22][23][24][25][26][27][28][29][30], as they do not suffer from the infamous sign problem of fermionic systems. However, QMC is usually restricted to groundstate calculations, although extensions to molecular properties [31][32][33][34][35] and excited states [36][37][38][39][40] have been developed. The rise of quantum computing can open alternative routes to groundstate calculations (and beyond) for many-boson systems, for instance based on superconducting circuits [41][42][43][44][45], cold-atom lattices [46,47] or photonic quantum devices [48][49][50][51][52][53][54][55] (such as Gaussian boson sampling experiments [48,49,52,53]), essentially used as analog quantum simulators.…”

Section: Introductionmentioning

confidence: 99%

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

Yalouz

Senjean

Miatto

et al. 2021

Quantum

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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.

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Excited‐State Calculations with Quantum Monte Carlo

Cited by 14 publications

References 92 publications

Accurate and Efficient Computation of Optical Absorption Spectra of Molecular Crystals: The Case of the Polymorphs of ROY

Accurate and Efficient Computation of Optical Absorption Spectra of Molecular Crystals: The Case of the Polymorphs of ROY

Stochastic Effective Core Potentials, toward Efficient Quantum Monte Carlo Simulations of Molecules with Large Atomic Numbers

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

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