Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates

Understand

Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms.

• For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the observable as a linear combination of measurable fragments.
• The main problem of this approach is a large number of measurements required for accurate sampling of the observable's expectation value.
• We consider several partitioning schemes based on grouping of commuting multi-qubit Pauli products with the goal of minimizing the number of measurements.