Optimization of variational-quantum-eigensolver measurement by partitioning Pauli operators using multiqubit Clifford gates on noisy intermediate-scale quantum hardware

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of Pauli operators allows for fewer mea-surements and an overall speedup of the measurement process. Using results from coloring random graphs, we give evidence for an upper bound on the expected minimum number of simultaneously measurable parts necessary to partition a set of Pauli operators. By expanding our gate set to allow multiqubit Clifford gates before measurement, we were able to cut down the number of measurements considerably compared to previous approaches. We conjecture that this improvement is, in general, linear with respect to the lengths of the Pauli operators. We conclude by demonstrating the feasibility of this approach by implementing the variational quantum eigensolver on the Aspen-4-4Q-A quantum processor unit. In doing so, we calculate the ground-state energies of H2 using fewer measurements than is possible with single-qubit gates with no statistically significant difference in accuracy.