Spin-preserving maps

Hello to you all!

I’m currently learning more about Givens rotations and how they can be used for quantum chemistry with quantum computing and while reading the PennyLane tutorial (Givens rotations for quantum chemistry — PennyLane documentation), I’ve realized that one of the Givens rotation used as an example (a single excitation from the ground state to the excited state with two electrons) is a spin-preserving map.

It says that “In the context of quantum chemistry, it is common to consider excitations on a fixed reference state and include only the excitations that preserve the spin orientation of the electron.”, I wanted to know why it would be the case.

Thank you for your response!

Hi @Mohamed_SO. The excitation operators are applied to a reference Slater determinant to form excited determinants that are used to construct the many-body wavefunction. See the configuration interaction and coupled cluster methods for more details. Now, excitation to orbitals with different spin results in excited determinants that have different total spin. In cases where the Hamiltonian operator does not explicitly contain spin, the corresponding matrix elements formed from these determinants are zero. You can also think of it as mixing, for instance, singlet and teriplet states in your wave function. Therefore, only those excitation operators are applied that excite electrons to spin-orbitals with the same spin. You can find a detailed explanation of this and the relevant concepts in Sec. 4.1-4.2 of Introduction to Computational Chemistry. Hope the explanation is helpful. Please let me know if you have other questions.