Research

From Symmetric Toeplitz Hamiltonians to Quantum Circuits Aug '25 arxiv

  supervised by Benoît Valiron, QuaCS team, LMF (Laboratoire Méthodes Formelles)

This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices M_k. These matrices are then classified, to achieve significant simplification, into, M_k when k is a power of two, and congruence classes with constant coefficients. Finally, the practical utility of this approach is demonstrated by applying it to a canonical problem in physics: the simulation of the one dimensional Poisson equation.

For more details, read the following report (less rigorous, more intuitive)