Contracted Quantum Eigensolvers for Quantum Simulation

Simulating many-body quantum systems poses a significant challenge and opportunity for near-term quantum computing. Here, we highlight a class of recently developed quantum contracted eigensolvers. We focus on an approach which aims to solve the anti-Hermitian part of the contracted Schrodinger equation (ACSE) on a quantum computer. Our method exhibits exponential cost reductions on a quantum computer, and leads to iterations with only polynomial scaling tomography in the construction of the reduced density matrices. We also highlight applications of a qubit-particle parametrization of a fermionic wavefunction. This allows for a reduction in the multi-qubit gate cost in our solution of the ACSE, while still maintaining a high level of accuracy. Finally, we explore applications of classical optimization techniques to the qACSE approach, and are able to demonstrate rapid convergence towards a solution of the ACSE across a variety of systems.