Quantum Simulation of Molecular Response Properties in the NISQ Era

Kumar, Ashutosh; Asthana, Ayush; Abraham, Vibin; Crawford, T. Daniel; Mayhall, Nicholas J.; Zhang, Yu; Cincio, Lukasz; Tretiak, Sergei; Dub, Pavel A.

doi:10.1021/acs.jctc.3c00731

Cited by 12 publications

(14 citation statements)

References 89 publications

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“…The self-consistent (SC) operators − , are constructed via a unitary transformation with the wave function active space ansatz bold-italicU = exp ( − t̂ false( bold-italicθ false) ) (recall subsection for our oo-UCC wave function) Ô normals normalc = bold-italicU Ô bold-italicU † Applying the self-consistent transformation to the orbital rotation operator yields terms of the form q̂ p q normals normalc false| 0 ⟩ = bold-italicU q̂ p q false| C S F ⟩ Since the orbital rotation operator now works directly on the reference CSF, the nonredundant parameter space is reduced to pq ∈ { v a i , ai , av i }, and the parameters removed are of the type { v i i , av a }.…”

Section: Theorymentioning

confidence: 99%

“…Finally, the projected (proj) operators , are Ô normalp normalr normalo normalj = Ô false| 0 ⟩ ⟨ 0 false| prefix− ⟨ 0 false| Ô false| 0 ⟩ and since q̂ † false| 0 ⟩ = 0 , the projection for the orbital rotation reduces to q̂ p r o j = q̂ | 0 false⟩ false⟨ 0 false| . The transformation of the active-space excitation operators does not lead to any similar reduction in the parameter space for any of the transformations.…”

Section: Theorymentioning

confidence: 99%

“…Note that some transformations of this kind have been used in the literature for the full-space equation of motion (EOM)/LR approaches, i.e., approaches without active space and orbital optimization. This includes naive, , self-consistent, − and projected full-space operators.…”

Section: Theorymentioning

confidence: 99%

“…After a few years where the focus of NISQ computations in quantum chemistry has been on ground-state preparation, the attention is nowadays progressively shifting toward other properties than ground-state energies, in particular toward linear response (LR) properties, such as excitation energies, transition strengths, and general linear response functions. − …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Ziems,

Kjellgren,

Reinholdt

et al. 2024

J. Chem. Theory Comput.

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Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136−9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resourceefficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Ziems,

Kjellgren,

Reinholdt

et al. 2024

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…Alternatively, the other emerging direction for calculating excited states on QC is based on the quantum subspace, showcased by quantum subspace expansion [43,[47][48][49][50], non-orthogonal VQE [51], equation of motions [52,53], and the quantum Krylov subspace (QKS) framework inspired by its classical analogs [54][55][56][57][58]. Current QKS methods utilize either real or imaginary time [55,56] evolutions to generate the Krylov subspace, which then is used to sample the low-lying spectrum of the Hamiltonian Ĥ.…”

Section: Introductionmentioning

confidence: 99%

Quantum Davidson algorithm for excited states

Tkachenko,

Cincio,

Boldyrev

et al. 2024

Quantum Sci. Technol.

Self Cite

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Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through either real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. In our research, we present an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. We employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules, utilizing quantum simulators. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuits. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

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