  Many-electron problems pose some of the greatest challenges in computational
science, with important applications across many fields of modern science.
Fermionic quantum Monte Carlo (QMC) methods are among the most powerful
approaches to these problems. However, they can be severely biased when
controlling the fermionic sign problem using constraints, as is necessary for
scalability. Here we propose an approach that combines constrained QMC with
quantum computing tools to reduce such biases. We experimentally implement our
scheme using up to 16 qubits in order to unbias constrained QMC calculations
performed on chemical systems with as many as 120 orbitals. These experiments
represent the largest chemistry simulations performed on quantum computers
(more than doubling the size of prior electron correlation calculations), while
obtaining accuracy competitive with state-of-the-art classical methods. Our
results demonstrate a new paradigm of hybrid quantum-classical algorithm,
surpassing the popular variational quantum eigensolver in terms of potential
towards the first practical quantum advantage in ground state many-electron
calculations.
