QCoder

Problem Statement

Implement the operation defined by the following matrix $A$ on a quantum circuit $\mathrm{qc}$ with $1$ qubit.

A = \ket{1}\bra{0}+\ket{0}\bra{1}

Constraints

In this problem, the state with different global phase will not be considered correct.
The submitted code must follow the specified format:

from qiskit import QuantumCircuit
 
 
def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
    # Write your code here:
 
    return qc

Hints

Open

A quantum state $\ket{\psi} = a_0 \ket{0} + a_1 \ket{1}$ can be represented as a column vector

\ket{\psi}=a_0\ket{0}+a_1\ket{1}=\begin{pmatrix}a_0\\a_1\end{pmatrix}.

The adjoint $\bra{\psi}$ of a quantum state $\ket{\psi}=a_0\ket{0}+a_1\ket{1}$ is defined as

\bra{\psi} = \ket{\psi}^{\dagger} = \begin{pmatrix}a_0^* & a_1^*\end{pmatrix}.

For quantum states $\ket{\psi}=\begin{pmatrix}a_0\\a_1\end{pmatrix}$ and $\bra{\phi}=\begin{pmatrix}b_0^* & b_1^*\end{pmatrix}$ , the inner product $\braket{\phi|\psi}$ is defined as

\braket{ \phi | \psi } = \begin{pmatrix} b_0^* & b_1^* \end{pmatrix} \begin{pmatrix} a_0 \\ a_1 \end{pmatrix} = b_0^* a_0 + b_1^* a_1.

Manipulating a quantum state is equivalent to multiplying a column vector by a unitary matrix from the left.

The outer product $\ket{\psi}\bra{\phi}$ of quantum states $\ket{\psi}=\begin{pmatrix}a_0\\a_1\end{pmatrix}$ and $\bra{\phi}=\begin{pmatrix}b_0^* & b_1^*\end{pmatrix}$ is defined as

\ket{\psi} \bra{\phi} = \begin{pmatrix} a_0 \\ a_1 \end{pmatrix} \begin{pmatrix} b_0^* & b_1^* \end{pmatrix} = \begin{pmatrix} a_0 b_0^* & a_0 b_1^* \\ a_1 b_0^* & a_1 b_1^*\end{pmatrix}

For arbitrary quantum state $\ket{\omega}$ , the following equation holds:

(\ket{\psi} \bra{\phi}) \ket{\omega} = \ket{\psi} \braket{ \phi | \omega } = \braket{ \phi | \omega } \ket{\psi}

B1: Bra-Ket Notated Gate

Problem Statement

Constraints

Hints