Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. We use a superconducting-qubit-based processor to apply the QSE approach to the ${\mathrm{H}}_2$ molecule, extracting both ground and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.