  An important measure of the development of quantum computing platforms has
been the simulation of increasingly complex physical systems. Prior to
fault-tolerant quantum computing, robust error mitigation strategies are
necessary to continue this growth. Here, we study physical simulation within
the seniority-zero electron pairing subspace, which affords both a
computational stepping stone to a fully correlated model, and an opportunity to
validate recently introduced ``purification-based'' error-mitigation
strategies. We compare the performance of error mitigation based on doubling
quantum resources in time (echo verification) or in space (virtual
distillation), on up to $20$ qubits of a superconducting qubit quantum
processor. We observe a reduction of error by one to two orders of magnitude
below less sophisticated techniques (e.g. post-selection); the gain from error
mitigation is seen to increase with the system size. Employing these error
mitigation strategies enables the implementation of the largest variational
algorithm for a correlated chemistry system to-date. Extrapolating performance
from these results allows us to estimate minimum requirements for a
beyond-classical simulation of electronic structure. We find that, despite the
impressive gains from purification-based error mitigation, significant hardware
improvements will be required for classically intractable variational chemistry
simulations.
