Evermore optimized simulations of fermionic systems on a quantum computer

In this work, we present an advanced compilation and optimization technique to reduce the number of two-qubit entangling gates used for the simulation of fermonic interactions on a quantum computer. Our optimization method greatly simplifies the procedure used in the state-of-the-art method, by mapping the quantum circuit optimization problem to well-studied optimization problems, such as graph vertex coloring problem and traveling salesman problem. This enables us to exploit the well-studied classical optimization algorithms and commercial solvers. We present the optimization results for the simulation of several small molecules and show that the number of quantum gates used can be saved up to 24\% over the state of the art. Our advanced compilation and optimization technique can straightforwardly be generalized to wider classes of near-term simulations of the ground state of a fermionic system or real-time simulations probing dynamical properties of a fermionic system.