# Observable grouping#

For sampling of observables expanded by Pauli operators, several methods have been developed to reduce number of measurements by dividing the Pauli operators into groups and simultaneously measuring Pauli operators in each group. When measuring by sampling (type of QuantumDevice is not EXACT_SIMULATOR), you can specify them as observable_grouping.

## Type#

The following types of ObservableGrouping are available (if no input is given, BITWISE_COMMUTING is set as the default value):

• BITWISE_COMMUTING [Kan17, Ver20]: Assign bitwise commutative Pauli operators to a group to be measured simultaneously. For example, $$X_0 Z_1 X_2 Z_3$$ and $$X_0 I_1 X_2 I_3$$ are bitwise commutative and are assigned to the same group. On the other hand, $$X_0 Z_1 X_2 Z_3$$ and $$X_0 Y_1 X_2 Y_3$$ are commutative but not bitwise commutative, so they will be assigned to different groups. Using this grouping method, the number of measurements can be reduced to 1/3 on average.

• NO_GROUPING: Assign one Pauli operator to each group.

## References#

[Kan17] “Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets”, A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink , J. M. Chow, J. M. Gambetta, Nature 549, 242 (2017)

[Ver20] “Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover”, V. Verteletskyi, T. Yen, A. F. Izmaylov, J. Chem. Phys. 152, 124114 (2020)

## Input example#

"observable_grouping": {
"type": "BITWISE_COMMUTING"
}