Quantum Fourier Transform¶

In this example, we will explore the Quantum Fourier Transform (QFT) circuit using recursion and iteration -- a convenient way to implement the QFT circuit using our high-level programming features.

To begin, we will import the qasm2 module from the bloqade package and the PyQrack backend from the bloqade.pyqrack module, which can be installed via

pip install bloqade[pyqrack]

or

pip install bloqade[pyqrack-cpu]

depending on the hardware and OS you have.

In [ ]:

import math

from bloqade import qasm2
from bloqade.pyqrack import PyQrack

import math from bloqade import qasm2 from bloqade.pyqrack import PyQrack

In the following, we will define the Quantum Fourier Transform (QFT) circuit using recursion inside a kernel function qft. The qft function takes two arguments: a quantum register qreg and an integer n representing the number of qubits we want to apply the QFT circuit to.

In [ ]:

pi = math.pi


@qasm2.extended
def qft(qreg: qasm2.QReg, n: int, k: int):
    if k == n:
        return qreg

    qasm2.h(qreg[k])
    for i in range(k + 1, n):
        qasm2.cu1(qreg[i], qreg[k], 2 * math.pi / 2**i)
    qft(qreg, n, k + 1)  # recursion
    return qreg

pi = math.pi @qasm2.extended def qft(qreg: qasm2.QReg, n: int, k: int): if k == n: return qreg qasm2.h(qreg[k]) for i in range(k + 1, n): qasm2.cu1(qreg[i], qreg[k], 2 * math.pi / 2**i) qft(qreg, n, k + 1) # recursion return qreg

Next, we will call this kernel function qft inside a main function to check if the QFT circuit is correctly implemented. We will use a quantum register of size 3.

In [ ]:

@qasm2.extended
def main():
    return qft(qasm2.qreg(3), 3, 0)

@qasm2.extended def main(): return qft(qasm2.qreg(3), 3, 0)

Finally, we will run the main function on the PyQrack backend and print the quantum register to see the final state of the qubits after applying the QFT circuit.

In [ ]:

device = PyQrack()
qreg = device.run(main)
print(qreg)

device = PyQrack() qreg = device.run(main) print(qreg)

we can also emit the QASM2 code for the main function and print it to see the QASM2 code that corresponds to the QFT circuit.

In [ ]:

from bloqade.qasm2.emit import QASM2  # noqa: E402
from bloqade.qasm2.parse import pprint  # noqa: E402

target = QASM2()
ast = target.emit(main)
pprint(ast)

from bloqade.qasm2.emit import QASM2 # noqa: E402 from bloqade.qasm2.parse import pprint # noqa: E402 target = QASM2() ast = target.emit(main) pprint(ast)