Purification-based quantum error mitigation of pair-correlated electron simulations

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 validate recently introduced “purification-based” error-mitigation strategies on physical simulation within the seniority-zero electron pairing subspace, which affords a computational stepping stone to a fully correlated model. 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). We study how the gain from error mitigation scales with the system size, and observe a polynomial suppression of error by echo verification and virtual distillation. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolation of these results suggests significant hardware improvements will be required for classically intractable variational chemistry simulations.