Riemannian quantum circuit optimization based on matrix product operators

Understand

We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods.

• Unlike previous approaches, our method imposes no symmetry assumptions, such as translational invariance, on the quantum systems.
• This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator.
• Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian.