#!/usr/bin/env python
# coding: utf-8

# # Compiling and simulating a 10-qubit Quantum Fourier Transform (QFT) algorithm
# 
# In this notebook, we simulate a 10-qubit Quantum Fourier Transform (QFT) algorithm.
# The QFT algorithm is one of the most important quantum algorithms in quantum computing.
# It is, for instance, part of the Shor algorithm for integer factorization.
# The following code defines a 10-qubit QFT algorithm using CNOT and single qubit rotations and runs the simulation both at the gate level and at the pulse level.

# In[1]:


from qutip import basis, fidelity
from qutip_qip.algorithms import qft_gate_sequence
from qutip_qip.device import LinearSpinChain
from qutip.ipynbtools import version_table
import qutip_qip

num_qubits = 10
# The QFT circuit
qc = qft_gate_sequence(num_qubits, swapping=False, to_cnot=True)
# Gate-level simulation
state1 = qc.run(basis([2] * num_qubits, [0] * num_qubits))
# Pulse-level simulation
processor = LinearSpinChain(num_qubits)
processor.load_circuit(qc)
state2 = processor.run_state(basis([2] * num_qubits,
                                   [0] * num_qubits)).states[-1]
fidelity(state1, state2)


# We plot the compiled pulses in the cell below.
# The pulses plotted implement the QFT algorithm represented in the native gates of the spin chain model, with single-qubit gates marked by rotations over the $x$- and $z$-axes and the iSWAP gate implemented through the spin-spin exchange interaction, marked by $g_i$.
# While the sign for single-qubit drive denotes the phase of the control pulse, the negative sign in the coupling strengths $g_i$ is only a result of the convention used in the definition of the interaction, defined in \cref{eq:ham spin chain}.

# In[2]:


def get_control_latex(model):
    """
    Get the labels for each Hamiltonian.
    It is used in the method method :meth:`.Processor.plot_pulses`.
    It is a 2-d nested list, in the plot,
    a different color will be used for each sublist.
    """
    num_qubits = model.num_qubits
    num_coupling = model._get_num_coupling()
    return [
        {f"sx{m}": r"$\sigma_x^{}$".format(m) for m in range(num_qubits)},
        {f"sz{m}": r"$\sigma_z^{}$".format(m) for m in range(num_qubits)},
        {f"g{m}": r"$g_{}$".format(m) for m in range(num_coupling)},
    ]


fig, axes = processor.plot_pulses(
    figsize=(5, 7), dpi=150, pulse_labels=get_control_latex(processor.model)
)
axes[-1].set_xlabel("$t$");


# In[3]:


print("qutip-qip version:", qutip_qip.version.version)
version_table()