Closed-Form Expressions for Unitaries of Spin-Adapted Fermionic Operators

TL;DR

This paper derives closed-form expressions for unitaries generated by spin-adapted operators, advancing the efficient enforcement of spin symmetry in quantum simulations of chemical systems.

Contribution

It provides the first closed-form formulas for unitaries of singlet spin-adapted excitations, addressing a key challenge in quantum chemistry simulations.

Findings

Derived closed-form expressions for spin-adapted unitaries.

Enables more efficient and symmetry-preserving quantum simulations.

Progress towards practical quantum algorithms for chemistry.

Abstract

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while na\"ive Trotterization schemes break spin symmetry. In this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalized single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.