Related Experiment Video
Updated: Jan 16, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
8.9K
Exact closed-form expressions for unitary spin-adapted fermionic singlet double excitation operators
Erik Rosendahl Kjellgren1, Karl Michael Ziems2,3, Peter Reinholdt1
1Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark.
The Journal of Chemical Physics
|October 3, 2025
Summary
Researchers developed exact formulas for anti-Hermitian spin-adapted singlet double excitation fermionic operators. This enables efficient quantum computing methods and guarantees convergence to specific spin symmetries for quantum devices.
Area of Science:
- Quantum computing
- Quantum chemistry
- Theoretical physics
Background:
- Efficient implementation of fermionic operators is crucial for quantum chemistry simulations.
- Maintaining spin symmetry is essential for accurate quantum mechanical calculations.
Purpose of the Study:
- To derive exact closed-form expressions for the matrix exponential of anti-Hermitian spin-adapted singlet double excitation fermionic operators.
- To facilitate the efficient implementation of these operators in quantum computing frameworks.
- To enable ansätze that guarantee convergence to specific spin symmetries.
Main Methods:
- Derivation of exact closed-form expressions for matrix exponentials.
- Application within unitary product state frameworks.
- Development of spin-adapted circuits for quantum devices.
Main Results:
- Obtained exact closed-form expressions for the matrix exponential of specific fermionic operators.
- Enabled efficient implementation on conventional quantum hardware.
- Ensured convergence to desired spin symmetries.
Conclusions:
- The derived expressions offer a pathway for efficient quantum computation of molecular properties.
- These methods can be applied to construct robust spin-adapted circuits for quantum computers.
- The work advances the development of quantum algorithms for chemistry and materials science.
Related Concept Videos
03:06The Pauli Exclusion Principle
58.9K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
58.9K
02:42Valence Bond Theory
11.2K
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
11.2K
01:03Atomic Nuclei: Nuclear Spin State Overview
1.9K
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
1.9K
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
48.1K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
48.1K
01:20Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
1.6K
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
1.6K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
2.3K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
2.3K