> For the complete documentation index, see [llms.txt](https://writeups.ayweth20.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://writeups.ayweth20.com/2025/404ctf-2025/algorithmique-quantique/grover-1-2.md).

# Grover (1/2)

**Catégorie:** Algorithmique Quantique - **Difficulté:** Facile

{% file src="/files/i7lXOAaSjG33Vcg1xoUe" %}

**Description:**

<figure><img src="https://4219205392-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fybn4btwQnvitOl9uXz9p%2Fuploads%2FqEUTUuhjdj6zqDLHcZmE%2Fimage.png?alt=media&amp;token=1737e588-1673-4ae1-9fa2-ee9f9e41580a" alt=""><figcaption></figcaption></figure>

Solution:

Voici le script de résolution du challenge :&#x20;

{% code fullWidth="false" %}

```python
import json
import requests

from machinerie import Circuit, create_grover  # fonctions fournies :contentReference[oaicite:0]{index=0}:contentReference[oaicite:1]{index=1}


def build_f1() -> Circuit:
    """f₁(x) = ¬x (sur 1 qubit de sortie)."""
    qc = Circuit(2, name="f1")
    qc.cx(0, 1)   # copie x
    qc.x(1)       # NOT
    return qc


def build_f2() -> Circuit:
    """f₂( x₀ x₁ ) = ¬x₁ (sur un 3ᵉ qubit)."""
    qc = Circuit(3, name="f2")
    qc.cx(1, 2)   # copie x₁
    qc.x(2)       # NOT
    return qc


def build_grover() -> Circuit:
    """
    Oracle + diffuseur pour la cible ‘10’.
    flag = [0, 1]  ➜ qubit0 doit valoir 0, qubit1 doit valoir 1 :contentReference[oaicite:2]{index=2}:contentReference[oaicite:3]{index=3}
    """
    return create_grover(
        flag=[0, 1],          # cible = ‘10’ (q₁ = 1, q₀ = 0)
        hadamard_middle=[0, 1],
        hadamard_end=[0, 1],
    )


def solve_grover_challenge() -> None:
    f1 = build_f1()
    f2 = build_f2()
    grover = build_grover()

    # Test local : doit tout mettre sur |10>
    verifier = Circuit(2)
    verifier.h([0, 1])          # état uniforme
    verifier.compose(grover, inplace=True)
    print("Mesure locale (attendu ≈ {'10': 1.0}):",
          verifier.get_measure(shots=1024, normalise=True))

    # Matrices aplaties à envoyer
    payload = {
        "f1": f1.get_flat_unitary(),
        "f2": f2.get_flat_unitary(),
        "grover": grover.get_flat_unitary(),
    }

    url = "https://causapscal-des-profondeurs.404ctf.fr/challenges/2"
    headers = {"Content-Type": "application/json", "Accept": "application/json"}
    r = requests.post(url, json=payload, headers=headers)
    print("Réponse serveur :", r.json())


if __name__ == "__main__":
    solve_grover_challenge()
```

{% endcode %}

Et voilà le résultat :&#x20;

<figure><img src="https://4219205392-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fybn4btwQnvitOl9uXz9p%2Fuploads%2FICw83C7adsHgs4LBWAcT%2Fimage.png?alt=media&amp;token=b74c2146-5b45-4ae6-acab-09e655ae1f73" alt=""><figcaption></figcaption></figure>

<details>

<summary>🚩FLAG</summary>

`404CTF{z0r_oU_XoR?_j3_N3_m_En_sOr_pLU5}`

</details>