Numerical analysis of quantum circuits for state preparation and unitary operator synthesis

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we maximum achievable fidelity as a function circuit size. This information allows us identify size specific target operation enumerate different configurations that allow perfect implementation operation. find there are large produce desired result, even at gates. also show entangling can be reduced if use multi-qubit instead gates, one might expect based on parameter counting calculations. In addition treating general case arbitrary states or operators, apply numerical approach special synthesizing Toffoli gate. used investigate any other task provides insight into tightness bounds in literature.