Symposium FTQC4NSc 2026: Pauli and Majorana Propagation Methods

Symposium FTQC4NSc 2026 Speaker: Prof. Zoë Holmes (EPFL) Abstract: Pauli and Majorana Propagation Methods for Supporting Chemistry and Materials Workflows on Quantum Hardware We present a method of integrating low-energy assumptions into a variety of quantum algorithms for physical simulation that leverages Hamiltonians represented as a sum of squares and spectral amplification. Spectral amplification minimizes query costs by useful uncertainty propagation when performing a parameter estimation task if the initial state is in the low-energy sector of a non-negative Hamiltonian. The non-negative Hamiltonian representations we utilize are sum-of-squares certificates on the lowest eigenvalue. This work connects non-commutative polynomial optimization to quantum algorithms and is demonstrated to lower quantum gate complexities when computing the ground state of strongly correlated electronic systems in first and second quantization. We will also highlight how sum-of-squares Hamiltonian representations can be used in classical electronic structure simulation with potentially reduced costs. This talk was presented at the Fault-Tolerant Quantum Computing for Natural Sciences Symposium 2026 in Heilbronn. For more information about FTQC4NSc 2026, please visit https://flaqship.eu/ftqc4nsc