Exact closed-form expression for unitary spin-adapted fermionic singlet double excitation operators

2025/05/01 by Erik Rosendahl Kjellgren, Kjellgren, Erik Rosendahl, Karl Michael Ziems +9
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum optics and atomic interactions #Magnetic properties of thin films

paper · pdf · doi:10.48550/arxiv.2505.00883

Abstract

We derive exact closed-form expressions for the matrix exponential of the anti-Hermitian spin-adapted singlet double excitation fermionic operators. These expressions enable the efficient implementation of such operators within unitary product state frameworks targeting conventional hardware, and allow for the implementation of ansatze that guarantee convergence to specific spin symmetries. Moreover, these exact closed-form expressions might also lay the groundwork for constructing spin-adapted circuits for quantum devices.

Related

• Closed-Form Expressions for Unitaries of Spin-Adapted Fermionic Operators
• Spin-Adapted Fermionic Unitaries: From Lie Algebras to Compact Quantum Circuits
• Exact closed-form unitary transformations of fermionic operators
• Exact Factorization of Unitary Transformations with Spin-Adapted Generators
• Spin-1/2 operators exactly mapped to spinful canonical Fermi operators present in two bands