Last week I was thrilled to attend the Quantum Computing Theory in Practice (QCTiP) conference in Oxford, where I got to present on joint work with Dr Nathan Fitzpatrick at Quantinuum! This is the Paldus Transform, our new algorithm for decomposing second-quantised fermionic Fock spaces on a quantum computer. In simple terms, it maps states with well-defined quantum numbers such as particle number, spin, and spin projection into a form where each is stored locally on a separate quantum register. This can be seen as a generalisation of the Schur Transform to second-quantised computational chemistry – similarly, it block-diagonalises Hamiltonian evolution obeying \(U(d) \times SU(2)\) duality discovered by Josef Paldus & co. in the 1970s.

The mathematics behind the Paldus transform is fascinating, and its applications potentially very powerful. It was a pleasure to talk about them in my presentation! Since our paper hit arXiv last year, there has been a lovely blog post by Quantinuum with a popular summary. I have also written a bit about the history of the underlying ideas in a LinkedIn post. Finally, I would like to give my thanks to Vojtěch Havlíček and his team at IBM Research, who invited me to speak about this work in a seminar last summer :)