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

Abstract

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems [1–3]. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth [4–11]. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model [12–17], and an opportunity to validate recently introduced “purification-based” error-mitigation strategies [8–10]. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification [10]) or in space (virtual distillation [8, 9]), 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.