Quantum Simulations beyond Electronic-Structure Methods: from Tensor Networks to Quantum Computing

The simulation of quantum many-body systems is emerging as one of the most promising targets for quantum computing.1 In fact, quantum hardware promises to exponentially reduce the com- putational cost of these simulations compared to classical computers. In chemistry, quantum- computing algorithms have been mostly designed for time-independent electronic-structure cal- culations. However, other classes of many-body problems are relevant for chemical simulations. This includes vibrational-structure,2–4 coupled vibrational-electronic, 5,6 and time-dependent cal- culations.7 In this contribution, we will first describe methods that we developed, based on the density matrix renormalization group (DMRG) theory, for studying quantum-chemical many- body systems beyond electronic-structure problems. We will show how these methods can target systems that are hard challenges for alternative state-of-the-art quantum-chemical many-body methods. They set, therefore, the bar that quantum-computing algorithms must overcome to yield a practical quantum advantage in quantum-chemical simulations, as we will critically dis- cuss for the case of molecular vibrational-structure calculations.