QCoder

Problem Statement

For an integer $k$ where $0 \leq k < 4$ , define $E(k)$ as follows:

\begin{aligned} E(0) &= I \otimes I \otimes I \\ E(1) &= X \otimes I \otimes I \\ E(2) &= I \otimes X \otimes I \\ E(3) &= I \otimes I \otimes X \end{aligned}

Here, $I$ is the $2 \times 2$ identity matrix, and $X$ is the $X$ gate.

I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix},\quad X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}

Given $\ket{\psi} = \alpha \ket{000} + \beta \ket{111}$ (where $\alpha$ and $\beta$ are arbitrary complex numbers), implement an oracle $O$ on a $5$ -qubit quantum circuit $\mathrm{qc}$ which satisfies the following condition:

(E(k) \otimes I \otimes I) \ket{\psi} \ket{00} \xrightarrow{O} (E(k) \otimes I \otimes I) \ket{\psi} \ket{k}

Constraints

Integers must be encoded by little-endian.
Global phase is ignored in judge.
The submitted code must follow the specified format:

from qiskit import QuantumCircuit
 
 
def solve() -> QuantumCircuit:
    qc = QuantumCircuit(5)
    # Write your code here:
 
    return qc

Hints

Open

$\ket{k}$ is expressed in little-endian. Therefore, writing $k = k_0 + 2k_1$ ( $k_0, k_1 \in \{0,1\}$ ), we have $\ket{k} = \ket{k_0}\ket{k_1}$ .

A3: Detection

Problem Statement

Constraints

Hints