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Exact Space Spin Factorisation of the Full Fermionic Wave Function under U(n) x SU(2): Part I

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If you have a question about this talk, please contact Chiara Leadbeater .

We present a rigorous factorization of the fermionic wave function within the framework of U(n)×SU(2) symmetry, extending the spin-free formalism of quantum chemistry introduced by Paldus. Using character theory and symmetric polynomial techniques, we construct a decomposition of the full fermionic Fock space, providing a first-principles derivation of its structure. Our approach reveals that the well-known Shavitt graph emerges naturally from a recursion relation derived from the Dual Cauchy identity of symmetric polynomials, offering new insights which will be built upon to construct a quantum algorithm.

This talk is part of the Quantum Computing for Quantum Chemistry series.

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