Multi Controlled U Gate

First Batch Mini Project: Multi Controlled U Gate

Here, we write a Qiskit function that takes two inputs: a positive integer $n$ and a matrix $U \in U(2)$ and outputs a quantum circuit on $n+1$ qubits, possibly with further ancillas, that implements a multi controlled $U$ gate, $C^nU$, that is $|x\rangle_nU|y\rangle_1$ if $x=(1, 1, \ldots, 1)$ and $|x\rangle_n|y\rangle_1$ otherwise. We do the imports as necessary and do the constructions. We follow this up with demonstrations regarding small $n$. We also do multiple verifications. Additionally, we discuss Resource Analysis and Resource Allocation. We also benchmark with various values for $n$. Lastly, we showcase an application with the multi controlled $Z$ as a Grover style Oracle. Note that both the Qiskit code and analysis of the quantum computation are in the Jupyter Notebook file.