Daniel Marti Dafcik, Nicholas Lee, Hugh G.A. Burton and David P. Tew
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction and the target eigenvector. This limits the power of quantum computers for solving challenging quantum chemistry problems, as typical initial states with a simple description have an overlap with the target Hamiltonian eigenstate that diminishes exponentially in the number of strongly correlated electrons. In this talk, we present a framework for understanding and approximating the low-energy wave functions in strongly correlated molecular systems in terms of a few spin-coupled states that are highly entangled, but highly structured. We also provide efficient quantum circuits for initial state preparation. Our approach avoids the need for expensive classical or quantum heuristics. Instead, we exploit symmetries to directly encode the dominant entanglement structure of the simulated system on quantum computers. For a range of popular quantum algorithms, including quantum phase estimation and several variational quantum algorithms, we demonstrate that using spin-coupled initial states drastically reduces the quantum resources required to compute strongly correlated ground and excited states.