QCoder Programming Contest 002

← Previous Problem Next Problem →

B4: Quantum Fourier Transform

Time Limit: 3 sec

Memory Limit: 512 MiB

Score: 200

Problem Statement

You are given an integer $n$ .
Implement the quantum Fourier transform (QFT) for $n$ qubits.

The quantum Fourier transform is defined as a $n$ -qubit oracle $\mathrm{QFT}$ acting on computational basis states as

\begin{equation} \ket{j}_n \xrightarrow{\mathrm{QFT}} \sqrt{\frac{1}{2^n}} \sum_{k=0}^{2^n-1} \exp{\left(\frac{2\pi i j k}{2^n}\right)} \ket{k}_n \nonumber \end{equation}

for any integer $j$ such that $0 \leq j < 2^n$ .

Constraints

$1 \leq n \leq 10$
The circuit depth must not exceed $25$ .
Integers are encoded by little-endian notation, i.e., $\ket{100} = 1 \neq \ket{001}$ .
Changes in the global phase are ignored.
The submitted code must follow the specified format:

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

Sample Input

$n = 2$
The implemented quantum circuit $\mathrm{qc}$ should perform the following transformation.

\ket{10} \xrightarrow{\mathrm{qc}} \frac{1}{\sqrt{4}} (\ket{00} + e^{\pi i / 2}\ket{10} + e^{\pi i}\ket{01} + e^{3 \pi i / 2}\ket{11})

Hints

Open

Please be aware that the circuit must be implemented assuming little-endian.

Please sign in to submit your answer.