C2: Controlled-T

Problem Statement

Using only Clifford gates, $T$ gate, and $CCX$ gate,

implement an oracle $U$ satisfying the following on a quantum circuit $\mathrm{qc}$ with $3$ qubits.

For any quantum state $\ket{\psi}_{2}$,

Here, $CT(0, 1)$ denotes the controlled-$T$ gate with qubit $1$ as the control qubit and qubit $2$ as the target qubit.

Constraints

• Only Clifford gates, $T$ gate, and $CCX$ gate can be used.
• The submitted code must follow the specified format:

from qiskit import QuantumCircuit
 
 
def solve() -> QuantumCircuit:
    qc = QuantumCircuit(3)
    # Write your code here:
 
    return qc

Hints