QCoder Programming Contest 006

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A1: Correction

Time Limit: 3 seconds

Memory Limit: 512 MiB

Score: 100 points

Problem Statement

Given an integer $k$ , implement an oracle $E(k)$ on a $3$ -qubit quantum circuit $\mathrm{qc}$ which satisfies the following condition:

\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}

where $I$ 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}

Constraints

$0 \leq k < 4$
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(k: int) -> QuantumCircuit:
    qc = QuantumCircuit(3)
    # Write your code here:
 
    return qc

Hints

Open

$E(1) = X \otimes I \otimes I$ means applying the $X$ gate to the $1$ st qubit.
You can apply the quantum gate $g$ to the $i$ -th qubit of the quantum circuit $\mathrm{qc}$ as follows:

qc.g(i - 1)

Please refer to Construct quantum circuits - Qiskit for quantum circuit examples and the What quantum gates can be used? for available quantum gates.

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