Strategies for reducing the number of controlled gates on noisy intermediate scale quantum circuits

We show that certain kind of controlled gates can be decomposed into a sequence of single-qubit operations when expectation values of some operators are needed. It is performed by decomposing the corresponding quantum channels into linear combination of single-qubit channels. Firstly, we discuss the usefulness of the presented method in variational algorithms which runs on quantum computer by showing that it can extract information about the derivatives of the parametrized state without adding ancilla qubit. It can also be applied for measuring the time correlation of observables in quantum simulations. Finally, we show that the method can decompose a large, in the number of qubits, quatnum circuit into smaller ones. Although the runtime of this method scales exponentially in the number of decompositions performed, it reduces the requirement on the hardware by reducing the number of gates and qubits in the trade-off of increased runtime.