def main():
qr, qc, crx, crz = setup()
# initialize state to teleport
vector_to_teleport = random_statevector(2)
qc = initialize_teleport_state(qc, tel_qbit=TELEPORT_QBIT, state=vector_to_teleport.data)
qc.barrier()
# craete bell pair, as q1 and q2 where q1 shared with Alice and q2 with Bob
qc = create_bell_pair(qc, a=A_QBIT, b=B_QBIT)
# find i, j value (which bell states craetes pair q0 and q1 together), i is related to state (q0) and
# j to Alice's entangeletn quibit q1
qc.barrier()
qc = alice_bell_measurement(qc, psi=TELEPORT_QBIT, a=A_QBIT)
qc.barrier()
# evaluate bell measurment of Alice's total state
# measured values are stored in crz and crx
qc = measure_and_send(qc, a=TELEPORT_QBIT, b=A_QBIT, bit_a=0, bit_b=1)
# apply gates regards to teleportation protocol theory
qc.barrier()
qc, crz, crx = bob_gates(qc, B_QBIT, crz=crz, crx=crx)
plot_teleport_state_vector(vector_to_teleport.data)
out_vector = q.execute(qc, STATE_VECTOR_BACKEND).result().get_statevector()
plot_bloch_multivector(out_vector)
# qc.draw("mpl")
plt.show()
def simulate_bloch_sphere(qc, title):
qc.draw(output='mpl')
backend = Aer.get_backend('statevector_simulator')
out_state = execute(qc, backend).result().get_statevector()
print(out_state)
plot_bloch_multivector(out_state)
# plot_bloch_multivector(out_state, title=title)
# plt.title(title)
plt.show()
def show_qc(qc: QuantumCircuit):
"""
Display the given state vector of the quantum circuit
"""
# print(qc.draw())
backend = Aer.get_backend('statevector_simulator')
out = execute(qc, backend).result().get_statevector()
plot_bloch_multivector(out).show()
return out
def controled_sdg_gate_bloch():
qc.h(0)
qc.x(1)
# Add controlled-Sdg gate
qc.cu1(-np.pi / 2, 0, 1)
statevector_backend = q.Aer.get_backend('statevector_simulator')
final_state = q.execute(qc, statevector_backend).result().get_statevector()
plot_bloch_multivector(final_state)
plt.show()
def ry_controller():
qc.x(0)
theta = np.pi / 4
qc.ry(theta / 2, t)
qc.cx(c, t)
qc.ry(-theta / 2, t)
qc.cx(c, t)
statevector_backend = q.Aer.get_backend('statevector_simulator')
final_state = q.execute(qc, statevector_backend).result().get_statevector()
plot_bloch_multivector(final_state)
plt.show()
def create_images(gate, theta=0.0, phi=0.0, lam=0.0):
# Set the loop parameters
steps = 20.0
theta_steps = theta / steps
phi_steps = phi / steps
lam_steps = lam / steps
n, theta, phi, lam = 0, 0.0, 0.0, 0.0
# Create image and animation tools
global q_images, b_images, q_filename, b_filename
b_images = []
q_images = []
b_filename = "animated_qubit"
q_filename = "animated_qsphere"
# The image creation loop
while n < steps + 1:
qc = QuantumCircuit(1)
if gate == "u3":
qc.u3(theta, phi, lam, 0)
title = "U3: \u03B8 = " + str(round(
theta, 2)) + " \u03D5 = " + str(round(
phi, 2)) + " \u03BB = " + str(round(lam, 2))
elif gate == "u2":
qc.u2(phi, lam, 0)
title = "U2: \u03D5 = " + str(round(phi, 2)) + " \u03BB = " + str(
round(lam, 2))
else:
qc.h(0)
qc.u1(phi, 0)
title = "U1: \u03D5 = " + str(round(phi, 2))
# Get the statevector of the qubit
# Create Bloch sphere images
plot_bloch_multivector(get_psi(qc),
title).savefig('images/bloch' + str(n) + '.png')
imb = Image.open('images/bloch' + str(n) + '.png')
b_images.append(imb)
# Create Q sphere images
plot_state_qsphere(psi).savefig('images/qsphere' + str(n) + '.png')
imq = Image.open('images/qsphere' + str(n) + '.png')
q_images.append(imq)
# Rev our loop
n += 1
theta += theta_steps
phi += phi_steps
lam += lam_steps
def blochSphere(self, circuit):
from qiskit import Aer
from qiskit import execute
from qiskit.visualization import plot_bloch_multivector
simulator = Aer.get_backend('statevector_simulator')
result = execute(circuit, backend=simulator).result()
statevector = result.get_statevector()
return plot_bloch_multivector(statevector)
def execute_circuit_sv(self):
sv_sim = Aer.get_backend('statevector_simulator')
result = execute(self.circuit, sv_sim).result()
state = result.get_statevector(self.circuit)
circuit_diagram = self.circuit.draw('mpl')
bloch_sphere = plot_bloch_multivector(state)
return circuit_diagram, state, bloch_sphere
def get_psi(circuit, title):
show_bloch = True
if show_bloch:
from qiskit.visualization import plot_bloch_multivector
backend = Aer.get_backend('statevector_simulator')
result = execute(circuit, backend).result()
psi = result.get_statevector(circuit)
print(title)
display(qc.draw('mpl'))
display(plot_bloch_multivector(psi))
def apply_gate():
"""Uses widget_state to apply the last selected gate, update
the code cell and prepare widget_state for the next selection"""
functionmap = {
'I': 'qc.iden',
'X': 'qc.x',
'Y': 'qc.y',
'Z': 'qc.z',
'H': 'qc.h',
'S': 'qc.s',
'T': 'qc.t',
'Sdg': 'qc.sdg',
'Tdg': 'qc.tdg',
'CX': 'qc.cx',
'CZ': 'qc.cz',
'SWAP': 'qc.swap'
}
gate = widget_state.current_gate
qubits = widget_state.qubits
widget_state.code += " "
if len(qubits) == 2:
widget_state.code += functionmap[gate]
widget_state.code += "({0}, {1})\n".format(qubits[0], qubits[1])
widget_state.qubits.pop()
elif widget_state.current_gate == 'Clear':
widget_state.code = ""
else:
widget_state.code += functionmap[gate] + "({})\n".format(qubits[0])
qc = QuantumCircuit(nqubits)
# This is especially awful I know, please don't judge me
exec(widget_state.code.replace(" ", ""))
qc.draw('mpl').savefig('circuit_widget_temp.svg', format='svg')
if bloch or dirac or qsphere:
ket = execute(qc, backend).result().get_statevector()
if bloch:
plot_bloch_multivector(ket, show_state_labels=True).savefig(
'circuit_widget_temp_bs.svg', format='svg')
if qsphere:
plot_state_qsphere(ket, show_state_labels=True).savefig(
'circuit_widget_temp_qs.svg', format='svg')
if dirac:
widget_state.statevec = ket
def draw_quantum_circuit(qc: QuantumCircuit, draw_circuit=True,
draw_unitary=True, draw_final_state=True,
draw_bloch_sphere=False, draw_q_sphere=False,
draw_histogram=False):
if draw_circuit:
# Visualize the quantum circuit
print('Quantum circuit:')
print(qc.draw())
if draw_unitary:
try:
# Visualize the unitary operator
backend = Aer.get_backend('unitary_simulator')
unitary = execute(qc, backend).result().get_unitary()
print('Unitary:')
for row in unitary:
print(' '.join([display_complex(elem) for elem in row]))
except QiskitError:
# If a qunatum circuit contains a measure operation, the process is
# not reversible anymore, and hence cannot be represented by a
# Unitary matrix. We just ignore this operation in that case.
pass
if draw_final_state or draw_bloch_sphere or draw_q_sphere:
# Visualize the final state
# final_state for 2 qubits = a |00> + b |01> + c |10> + d |11>
backend = Aer.get_backend('statevector_simulator')
final_state = execute(qc, backend).result().get_statevector()
if draw_final_state:
print('Final state:')
for elem in final_state:
print(display_complex(elem))
if draw_bloch_sphere:
plot_bloch_multivector(final_state).show()
if draw_q_sphere:
plot_state_qsphere(final_state).show()
if draw_histogram:
backend = Aer.get_backend('statevector_simulator')
results = execute(qc, backend).result().get_counts()
plot_histogram(results).show()
def qiskit():
# Plotting Single Bloch Sphere
plot_bloch_vector([0, 1, 0], title='Bloch Sphere')
# Building Quantum Circuit to use for multiqubit systems
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
# Plotting Multi Bloch System
state = Statevector.from_instruction(qc)
plot_bloch_multivector(state, title="New Bloch Multivector")
# Plotting Bloch City Scape
plot_state_city(state,
color=['midnightblue', 'midnightblue'],
title="New State City")
# Plotting Bloch Pauli Vectors
plot_state_paulivec(state, color='midnightblue', title="New PauliVec plot")
def not_corrected(error, ry_error, rz_error):
# Non-corrected code
qco = QuantumCircuit(1, 1)
print("\nOriginal qubit, in state |0>")
display(plot_bloch_multivector(get_psi(qco)))
display(plot_state_qsphere(get_psi(qco)))
# Add error
add_error(error, qco, ry_error, rz_error)
print("\nQubit with error...")
display(plot_bloch_multivector(get_psi(qco)))
display(plot_state_qsphere(get_psi(qco)))
qco.measure(0, 0)
display(qco.draw('mpl'))
job = execute(qco, backend, shots=1000)
counts = job.result().get_counts()
print("\nResult of qubit error:")
print("-----------------------")
print(counts)
def qgate_out(circuit, start):
# Print the circuit
psi = get_psi(circuit)
if start != "n":
print("\nCircuit:")
print("--------")
print(circuit)
print("\nState vector:")
print("-------------")
print(np.around(psi, decimals=3))
display(plot_bloch_multivector(psi))
if circuit.num_qubits > 1 and gate in control_gates:
display(plot_state_qsphere(psi))
return (psi)
def s_vec(circuit):
backend = Aer.get_backend('statevector_simulator')
print(circuit.num_qubits,
"qubit quantum circuit:\n------------------------")
print(circuit)
psi = execute(circuit, backend).result().get_statevector(circuit)
print("State vector for the", circuit.num_qubits, "qubit circuit:\n\n",
psi)
print("\nState vector as Bloch sphere:")
display(plot_bloch_multivector(psi))
print("\nState vector as Q sphere:")
display(plot_state_qsphere(psi))
measure(circuit)
input("Press enter to continue...\n")
def get_psi(circuit, vis):
from qiskit.visualization import plot_bloch_multivector, plot_state_qsphere
from qiskit import Aer, execute
global psi
backend = Aer.get_backend('statevector_simulator')
psi = execute(circuit, backend).result().get_statevector(circuit)
if vis == "Q":
display(plot_state_qsphere(psi))
elif vis == "M":
print(psi)
elif vis == "B":
display(plot_bloch_multivector(psi))
vis = ""
print_psi(psi)
return (psi)
def auto_bloch():
# Graphical representation of the Bloch Spheres for the game sequence HXH
qc = QuantumCircuit(4, 1)
# Prepare each qubit to visualize the states after each step
# qc.x(1) would change the initial position of q1 and results in different superposition
qc.h(1) # Qubit 1 - superposition after H gate
qc.h(2)
qc.x(2) # Qubit 2 - superposition after H and X gate (similar after H and iden)
qc.h(3)
qc.x(3)
qc.h(3) # Qubit 3 - result head after H, X and H
qc.measure([3], [0]) # Measure qubit 3 - would colapse if in s#perposition
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
print ("qubit0: initial position, qubit1: applying H, qubit2: applying X (after H), qubit3: applying H (after X and H)")
return plot_bloch_multivector(job.get_statevector(qc)) # Visualize quantum states
def show_multivector(coords):
qc = qiskit.QuantumCircuit(1)
non_normalized = np.array([complex(*coords[0:2]), complex(*coords[2:4])])
# Normalize each component
part_normalized = np.nan_to_num(non_normalized /
np.abs(non_normalized)) # nan -> 0
# Normalize all components
initial_state = part_normalized / np.linalg.norm(part_normalized)
qc.initialize(initial_state, 0)
backend = qiskit.Aer.get_backend('statevector_simulator')
out = qiskit.execute(qc, backend).result().get_statevector()
plt = plot_bloch_multivector(out)
return visualizer._export_png(plt)
def personal_bloch(moveA1, moveB1, moveA2):
# Graphical representation of the Bloch Spheres for the game sequence of the player
qc = QuantumCircuit(4, 1)
# Prepare each qubit to visualize the states after the according moves
# 1. move of A
if moveA1 == 0 :
qc.iden(1)
qc.iden(2)
qc.iden(3)
elif moveA1 == 1 :
qc.x(1)
qc.x(2)
qc.x(3)
elif moveA1 == 2 :
qc.h(1)
qc.h(2)
qc.h(3)
# 1. move of B
if moveB1 == 0 :
qc.iden(2)
qc.iden(3)
elif moveB1 == 1 :
qc.x(2)
qc.x(3)
# 2. move of A
if moveA2 == 0 :
qc.iden(3)
elif moveA2 == 1 :
qc.x(3)
elif moveA2 == 2 :
qc.h(3)
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
print('Your moves were: ',moveA1, moveB1, moveA2)
print('The states of the qubits for this game sequence can be visualized as follows:')
return plot_bloch_multivector(job.get_statevector(qc)) # Visualize quantum states
def plot_2_qubits():
fig = plot_bloch_multivector([0, 1, 0, 0])
fig.savefig('png/out.png')
plt.close()
def getBlochSphere(qc):
'''plot multi qubit bloch sphere'''
vec = getStateVector(qc)
return plot_bloch_multivector(vec)
def update_output():
out_state = execute(qc,backend).result().get_statevector()
if qsphere:
image.value = plot_state_qsphere(out_state)
else:
image.value = plot_bloch_multivector(out_state)
from math import pi
#gates = operations that changes qubits!
# Pauli gate!!
# multiply qubit's statevector by the gate to see the effect!!
# 1 qubit!!
quantum_circuit = QuantumCircuit(1)
quantum_circuit.x(0)
quantum_circuit.draw('mpl')
plt.show()
# plot_bloch_multivector takes in the qubit's statevector instead of the Bloch vector!!
backend = Aer.get_backend('statevector_simulator')
res= execute(quantum_circuit, backend).result().get_statevector()
plot_bloch_multivector(res)
plt.show()
# Pauli Y and Z gates ==> rotations about the y and z axes!!
quantum_circuit.y(0)
quantum_circuit.z(0)
plt.show()
# but these gates operate very similar to classical bits ==> want to instead use superposition!!
# use Hadamard gate instead!
# superposition of |0> and |1> ==> hadamard gate
quantum_circuit.h(0)
quantum_circuit.draw('mpl')
plt.show()
plot_histogram([counts, second_counts], legend=legend)
plot_histogram([counts, second_counts],
legend=legend,
sort='desc',
figsize=(15, 12),
color=['orange', 'black'],
bar_labels=False)
from qiskit.visualization import plot_state_city, plot_bloch_multivector
from qiskit.visualization import plot_state_paulivec, plot_state_hinton
from qiskit.visualization import plot_state_qsphere
backend = BasicAer.get_backend('statevector_simulator')
result = execute(bell, backend).result()
psi = result.get_statevector(bell)
plot_state_city(psi)
plot_state_hinton(psi)
plot_state_qsphere(psi)
plot_state_paulivec(psi)
plot_bloch_multivector(psi)
plot_state_city(psi, title="My City", color=['black', 'orange'])
plot_state_hinton(psi, title="My Hinton")
However, there are systems of qubits whose state cannot be described as the tensor product of its constituent sub-systems.
Such systems are called "entangled" in nature.
This property of entanglement is one of the most fundamentally important quantum mechanical property and is exploited a great deal in various of use cases.
For example, let us take the quantum state as described below
\begin{equation}
|\psi\rangle = a|00\rangle + b|11\rangle \\
a,b \neq 0
\end{equation}
This state cannot be expressed as a tensor product of $2$ qubits, and, hence, is an entangled state.
qcE = QuantumCircuit(2)
qcE.initialize([1/2**0.5,0,0,1/2**0.5], [0,1])
qcE.draw()
backend = Aer.get_backend('statevector_simulator')
result = execute(qcE,backend).result()
out_state = result.get_statevector()
print(out_state)
plot_bloch_multivector(out_state) # Qubits are Not Separable
## Bell States
A commonly used set of entangled states which are orthogonal to each other is the set of Bell states which is
\begin{equation}
|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}} \\
|\Phi^-\rangle = \frac{|00\rangle - |11\rangle}{\sqrt{2}} \\
|\Psi^+\rangle = \frac{|01\rangle + |10\rangle}{\sqrt{2}} \\
|\Psi^-\rangle = \frac{|01\rangle - |10\rangle}{\sqrt{2}}
\end{equation}
statevec = result.get_statevector()
nr_qubits = circuit.qregs[0].size
nr_cbits = circuit.cregs[0].size
circuit.measure(list(range(nr_qubits)), list(range(nr_cbits)))
qasm_result = q.execute(circuit, backend=qasm_simulator,
shots=2**12).result()
counts = qasm_result.get_counts()
return statevec, counts
def normalize_vector(vector: List) -> List:
norm = sqrt(sum([abs(x)**2 for x in vector]))
return [x / norm for x in vector]
qc = q.QuantumCircuit(1, 1) # Create a quantum circuit with one qubit
initial_state = normalize_vector([sqrt(1 / 3), sqrt(2 / 3)])
# initial_state = normalize_vector([sqrt(1 / 3), 1j * sqrt(2 / 3)])
qc.initialize(initial_state,
0) # Apply initialisation operation to the 0th qubit
statevec, counts = do_job(qc)
print(statevec)
plot_bloch_multivector(statevec).show()
# plot_histogram([counts]).show()
qc.measure_all()
statevec, counts = do_job(qc)
print(statevec)
plot_bloch_multivector(statevec).show()
return c
n = int(input("Enter the number of qbits : ")) # number of input bits
y = int(
input("Choose 1 if you want balanced or 0 if you want constant function")
) #function selection
circuit = q.QuantumCircuit(n + 1,
n + 1) #quantumbits = n+1 and classicalbits=n+1
circuit.x(n)
circuit.barrier() #Used for better visualization
circuit = hadamard(circuit)
circuit.h(n)
circuit.barrier()
if y == 1:
circuit = blackbox_balanced(circuit) #calling the balanced function
if y == 0:
circuit = blackbox_constant(circuit) #calling the constant function
circuit.barrier()
circuit = hadamard(circuit)
circuit.draw(output='mpl', filename='djckt.png')
originalstate = q.execute(circuit,
backend=statevec_sim).result().get_statevector()
circuit.measure(
[i for i in range(n)],
[i for i in range(n)]) #measuring n quantum bits to n classical bits
original_count = q.execute(circuit, backend=qasm_sim).result().get_counts()
print(circuit)
plot_bloch_multivector(originalstate).show()
plot_histogram(original_count).show()
\begin{equation}
|\psi\rangle = \alpha|0\rangle + e^{i\phi}\beta|1\rangle
\end{equation}
For normalisation, we know that $\sqrt{\alpha^2 + \beta^2} = 1$.
Hence, we can describe $\alpha$ and $\beta$ using a single variable $\theta$ as $\alpha = \cos{\tfrac{\theta}{2}}$ and $\beta=\sin{\tfrac{\theta}{2}}$.
So, for real $\theta$ and $\phi$, we get
\begin{equation}
|\psi\rangle = \cos{\tfrac{\theta}{2}}|0\rangle + e^{i\phi}\sin{\tfrac{\theta}{2}}|1\rangle
\end{equation}
Using $\theta$ and $\phi$ as the polar coordinates, we can map any single qubit state to a point on a sphere of radius $1$.
This sphere is called the Bloch Sphere.
plot_bloch_multivector([0,0,1,0])
plot_bloch_multivector([1/2**0.5,1/2**0.5])
## Rotation Gates
With respect to the Bloch Sphere (defined above), we have the rotation gates along the 3 axes, namely RX, RY and RZ.
These gates perform a rotation of the qubit vector along the specified axis by an angle $\theta$.
\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}RX(\theta) =
\begin{pmatrix}
\cos{\th} & -i\sin{\th} \\
-i\sin{\th} & \cos{\th}
\end{pmatrix}\end{split}\end{aligned}
\end{align}
from math import sqrt, pi
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import plot_bloch_multivector
# change alpha beta as you want
alpha = 1 / sqrt(2)
beta = 1j / sqrt(2)
# 2D complex vector representing the quantum state
vector = [alpha, beta]
# create a quantum circuit with only one qubit
qc = QuantumCircuit(1)
# initialzie the qubit as the vector we defined
# arg 0 is the index of the only qubit we created
qc.initialize(vector, 0)
# simulate the state
# note that statevector_simulator is used for calculating statevector (Quantum State)
backend = BasicAer.get_backend('statevector_simulator')
result = execute(qc, backend).result()
state = result.get_statevector(qc)
# plot the state on a Bloch sphere
plot_bloch_multivector(state)
def qonduit_visualization_state_plot_bloch_multivector(state):
return interactive(lambda sv: display(plot_bloch_multivector(sv)),
sv=fixed(state))