1.1.1 - Python Code for Circle Notation

Unfortunately, programming frameworks such IBM Qiskit and Google's Cirq don't support the circle notation for visualizing. However, we can write a simple Python code to visualize the quantum states. 

For instance, in Qiskit, to obtain the complex numbers of your quantum simulation, you can call the IBM Qiskit method:

state = sim.run(qobj).result().get_statevector()

You can check the code below to implement the circular notation for qubits in Python. In this example, we store the quantum state vector in a complex-valued array in the Qubit system class, just for demonstration purposes. For the visualization, you can check the viz2 function.

import numpy as np
import matplotlib
from matplotlib import pyplot as plt, patches
import cmath, math
import random
import sys
...

class QubitSystem:

    # init_state = initial state
    # n_qubits = number of the qubits in the system
    def __init__(self, n_qubits=1,label='qs X'):
        self.n_qubits = n_qubits
        self.n_states = 2**n_qubits
        self.label = label
        

        print("Quantum System Allocated")
        print("Number of qubits = ", self.n_qubits)
        print("Number of possible states = ", self.n_states)
        
        # allocate qubit system as an array of complex numbers
        self.qubit = np.zeros((self.n_states),dtype=np.complex)
        self.ampli_qubit = np.zeros((self.n_states),dtype=np.float)
        self.phase_qubit = np.zeros((self.n_states),dtype=np.float)

...

# Use Circle Notation
def viz2(self):
        # calculate amplitude and phase
        # calculate the amplitude and phase of the states
        self.prob_qubit = np.absolute(self.qubit)
        self.phase_qubit = np.angle(self.qubit)
        # viz par
        rows = int(math.ceil(self.n_states / 8.0))
        cols = min(self.n_states, 8)
        fig, axs = plt.subplots(rows, cols)
        for col in range(cols):
            # amplitude area
            circleExt = matplotlib.patches.Circle((0.5, 0.5), 0.5, color='gray',alpha=0.1)
            circleInt = matplotlib.patches.Circle((0.5, 0.5), self.prob_qubit[col]/2, color='b',alpha=0.3)
            axs[col].add_patch(circleExt)
            axs[col].add_patch(circleInt)
            axs[col].set_aspect('equal')
            state_number = "|" + str(col) + ">"
            axs[col].set_title(state_number)
            xl = [0.5, 0.5 + 0.5*self.prob_qubit[col]*math.cos(self.phase_qubit[col] + np.pi/2)]
            yl = [0.5, 0.5 + 0.5*self.prob_qubit[col]*math.sin(self.phase_qubit[col] + np.pi/2)]
            axs[col].plot(xl,yl,'r')
            axs[col].axis('off')
      plt.show()