add pulse-level notebooks

Author: christian512

tutorials-v4/pulse-level-circuit-simulation/qip-10-qubit-QFT-algorithm.md

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+---
+jupyter:
+  jupytext:
+    text_representation:
+      extension: .md
+      format_name: markdown
+      format_version: '1.3'
+      jupytext_version: 1.13.8
+  kernelspec:
+    display_name: Python 3 (ipykernel)
+    language: python
+    name: python3
+---
+
+# 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.
+
+```python
+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}.
+
+```python
+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("$t$");
+```
+
+```python
+print("qutip-qip version:", qutip_qip.version.version)
+version_table()
+```