Variational Quantum Annealing for Quantum Chemistry

We introduce a variational quantum annealing (VarQA) algorithm for electronic structure theory, in which we use the quantum annealer as a sampler and prepare an ansatz state through its statistics. We also introduce a strategy called the ``digitizer" for searching the space of variational parameters efficiently. We demonstrate the effectiveness of VarQA by evaluating the ground-state potential energy surface for molecules with up to $20$ spin orbitals as well as an excited-state potential energy surface. This approach resembles the workings of the Quantum Boltzmann Machines (QBMs), but is generalized to handle distributions beyond the Boltzmann distribution. Using Pauli-string algebraic techniques that connect quantum computer bitstrings with the Hamiltonian, one can efficiently sample the Hamiltonian's expectation value with low memory overhead. In VarQA, with the number of required logical qubits equal to the number of spin orbitals, a fully connected quadratic Ising Hamiltonian can be readily implemented in a large-scale quantum annealer as a scalable ansatz for electronic structure calculations.