Google Research

Compressing Many-Body Fermion Operators Under Unitary Constraints

Journal of Chemical Theory and Computation (2022)


The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising interaction type circuits. These circuits arise from factorizing the two-body operators generating those unitaries as a sum of squared one-body operators that are simulated using product formulas. We introduce a numerical algorithm for performing this factorization that has an iteration complexity no worse than single particle basis transformations of the two-body operators and often results in many times fewer squared one-body operators in the sum of squares compared to the analytical decompositions. As an application of this numerical procedure, we demonstrate that our protocol can be used to approximate generic unitary coupled cluster operators and prepare the necessary high-quality initial states for techniques (like ADAPT-VQE) that iteratively construct approximations to the ground state.

Research Areas

Learn more about how we do research

We maintain a portfolio of research projects, providing individuals and teams the freedom to emphasize specific types of work