Quantum computed moments correction to variational estimates

The variational principle of quantum mechanics is an important hybrid quantum algorithm in many applications. However, as the problem size grows, so does the trial-state circuit and quantum logic errors can easily overwhelm the quality of the results. Here we present an approach (arxiv.org/abs/2009.13140) based on quantum computed Hamiltonian moments <H^n>, which provide a correction to the variational result <H> for the ground-state energy of a given problem. Estimates of the ground-state energy are obtained from the computed moments using the infinum theorem from Lanczos cumulant expansions. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5x5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were computed to fourth order with respect to an antiferromagnetic trial-state. A comparison with benchmark variational calculations showed that the infinum estimate not only consistently outperformed the benchmark variational approach for the same trial-state, but also displayed a high degree of stability against trial-state variation, quantum gate errors and shot noise for this problem.