Simplified projection on total spin zero for state preparation on quantum computers
Abstract
We introduce a simple algorithm for projecting on $J=0$ states of a manybody system by performing a series of rotations to remove states with angular momentum projections greater than zero. Existing methods rely on unitary evolution with the twobody operator $J^2$, which when expressed in the computational basis contains many complicated Pauli strings requiring Trotterization and leading to very deep quantum circuits. Our approach performs the necessary projections using the onebody operators $J_x$ and $J_z$. By leveraging the method of Cartan decomposition, the unitary transformations that perform the projection can be parameterized as a product of a small number of twoqubit rotations, with angles determined by an efficient classical optimization. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of eveneven nuclei by projecting onto the $J=0$ component of deformed HartreeFock states. We estimate the resource requirements in terms of the universal gate set {$H$,$S$,CNOT,$T$} and briefly discuss a variant of the algorithm that projects onto $J=1/2$ states of a system with an odd number of fermions.
 Publication:

arXiv eprints
 Pub Date:
 October 2024
 DOI:
 10.48550/arXiv.2410.02848
 arXiv:
 arXiv:2410.02848
 Bibcode:
 2024arXiv241002848R
 Keywords:

 Quantum Physics;
 Nuclear Theory
 EPrint:
 13 pages, 3 figures