An approach to establish the connection between configuration and<i>su</i>(<i>n</i>+ 1) algebraic spaces in molecular physics: application to ammonia

Santiago, R. D.; Arias, J. M.; Gómez‐Camacho, J.; Lemus, R.

doi:10.1080/00268976.2017.1358829

Cited by 8 publications

(4 citation statements)

References 24 publications

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“…Finally, we comment on the possible extension of vibronic BS to go beyond the harmonic picture of the oscillators and the Condon approximation for the transition dipole moment. For the former, we would be able to incorporate the simple anharmonicity by a Morse oscillator [16,17]. For the latter, one can approximate the non-Condon operator [18] as a unitary operator so that the current vibronic boson sampling setup can be simply used.…”

Section: Discussionmentioning

confidence: 99%

Quantum Computing for Molecular Vibronic Spectra and Gaussian Boson Sampling

Chin

Huh

2018

J. Phys.: Conf. Ser.

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Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review, we discuss the correspondence relation between BS and MVS and briefly introduce the experimental demonstrations of the molecular spectroscopic process using quantum devices. The similarity of the two theories results in another BS setup, which is called "vibronic BS". The hierarchical structure of vibronic BS, which includes the original BS and other Gaussian BS, is also

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Section: Discussionmentioning

confidence: 99%

Quantum Computing for Molecular Vibronic Spectra and Gaussian Boson Sampling

Chin

Huh

2018

J. Phys.: Conf. Ser.

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“…Since both operators (19) and (20) preserve the angular momentum we can obtain their matrix representation for a given l and m in the N-dimensional space defined by…”

Section: Ho-dvr Approachmentioning

confidence: 99%

“…, 1 or 0, and the usual reduction SO(3) ⊃ SO(2) given by −l ≤ m ≤ l. It is clear that the N-dimensional space (21) is not complete, but it establishes a space to carry our the calculations in an approximate way. Explicitly the matrix elements of the operators (19) and (20) in dimensionless units turn out to be…”

Section: Ho-dvr Approachmentioning

confidence: 99%

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Algebraic DVR Approaches Applied to Describe the Stark Effect

et al. 2020

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Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r2 and p2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n=2,3 with m=0.

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Unitary group approach for effective potentials in 2D systems: Application to carbon suboxide C3O2

Rodríguez-Arcos

Lemus

2018

Chemical Physics Letters

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An approach to establish the connection between configuration andsu(n+ 1) algebraic spaces in molecular physics: application to ammonia

Cited by 8 publications

References 24 publications

Quantum Computing for Molecular Vibronic Spectra and Gaussian Boson Sampling

Quantum Computing for Molecular Vibronic Spectra and Gaussian Boson Sampling

Algebraic DVR Approaches Applied to Describe the Stark Effect

Unitary group approach for effective potentials in 2D systems: Application to carbon suboxide C3O2

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