def bloch_states(rho):
"""Return the values of the Bloch vectors for a given state.
Taken from plot_bloch_multivector in
qiskit.visualization.state_visualization.
"""
if rho.ndim == 1:
rho = np.outer(rho, np.conj(rho))
num = int(np.log2(len(rho)))
ret = []
for i in range(num):
pauli_singles = [
Pauli.pauli_single(num, i, "X"),
Pauli.pauli_single(num, i, "Y"),
Pauli.pauli_single(num, i, "Z"),
]
ret.append(
list(
map(
lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles,
)))
return ret
def plot_state(quantum_state, method='city', filename=None):
"""Plot the quantum state.
Args:
quantum_state (ndarray): statevector or density matrix
representation of a quantum state.
method (str): Plotting method to use.
filename (str): the output file to save the plot as. If specified it
will save and exit and not open up the plot in a new window. If
`bloch` method is used a `-n` will be added to the filename before
the extension for each qubit.
Raises:
VisualizationError: if the input is not a statevector or density
matrix, or if the state is not an multi-qubit quantum state.
"""
# Check if input is a statevector, and convert to density matrix
rho = np.array(quantum_state)
if rho.ndim == 1:
rho = np.outer(rho, np.conj(rho))
# Check the shape of the input is a square matrix
shape = np.shape(rho)
if len(shape) != 2 or shape[0] != shape[1]:
raise VisualizationError("Input is not a valid quantum state.")
# Check state is an n-qubit state
num = int(np.log2(len(rho)))
if 2**num != len(rho):
raise VisualizationError("Input is not a multi-qubit quantum state.")
if method == 'city':
plot_state_city(rho, filename=filename)
elif method == "paulivec":
plot_state_paulivec(rho, filename=filename)
elif method == "qsphere":
plot_state_qsphere(rho, filename=filename)
elif method == "bloch":
orig_filename = filename
for i in range(num):
if orig_filename:
filename_parts = orig_filename.split('.')
filename_parts[-2] += '-%d' % i
filename = '.'.join(filename_parts)
print(filename)
pauli_singles = [
Pauli.pauli_single(num, i, 'X'),
Pauli.pauli_single(num, i, 'Y'),
Pauli.pauli_single(num, i, 'Z')
]
bloch_state = list(
map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles))
plot_bloch_vector(bloch_state,
"qubit " + str(i),
filename=filename)
elif method == "wigner":
plot_wigner_function(rho, filename=filename)
elif method == "hinton":
plot_hinton(rho, filename=filename)
def test_pauli_single(self):
"""Test pauli single."""
num_qubits = 5
pz = Pauli.pauli_single(num_qubits, 2, 'Z')
self.assertTrue(pz.to_label(), 'IIIZI')
py = Pauli.pauli_single(num_qubits, 4, 'Y')
self.assertTrue(py.to_label(), 'IYIII')
px = Pauli.pauli_single(num_qubits, 3, 'X')
self.assertTrue(px.to_label(), 'IIXII')
def plot_bloch_multivector(rho, title='', figsize=None):
"""Plot the Bloch sphere.
Plot a sphere, axes, the Bloch vector, and its projections onto each axis.
Args:
rho (ndarray): Numpy array for state vector or density matrix.
title (str): a string that represents the plot title
figsize (tuple): Has no effect, here for compatibility only.
Returns:
Figure: A matplotlib figure instance if `ax = None`.
Raises:
ImportError: Requires matplotlib.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
num = int(np.log2(len(rho)))
width, height = plt.figaspect(1 / num)
fig = plt.figure(figsize=(width, height))
for i in range(num):
ax = fig.add_subplot(1, num, i + 1, projection='3d')
pauli_singles = [
Pauli.pauli_single(num, i, 'X'),
Pauli.pauli_single(num, i, 'Y'),
Pauli.pauli_single(num, i, 'Z')
]
bloch_state = list(
map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles))
plot_bloch_vector(bloch_state,
"qubit " + str(i),
ax=ax,
figsize=figsize)
fig.suptitle(title, fontsize=16)
plt.close(fig)
return fig
def iplot_bloch_multivector(rho, figsize=None):
""" Create a bloch sphere representation.
Graphical representation of the input array, using as much bloch
spheres as qubit are required.
Args:
rho (array): State vector or density matrix
figsize (tuple): Figure size in pixels.
"""
# HTML
html_template = Template("""
<p>
<div id="content_$divNumber" style="position: absolute; z-index: 1;">
<div id="bloch_$divNumber"></div>
</div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
data = $data;
dataValues = [];
for (var i = 0; i < data.length; i++) {
// Coordinates
var x = data[i][0];
var y = data[i][1];
var z = data[i][2];
var point = {'x': x,
'y': y,
'z': z};
dataValues.push(point);
}
require(["qVisualization"], function(qVisualizations) {
// Plot figure
qVisualizations.plotState("bloch_$divNumber",
"bloch",
dataValues,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
# Process data and execute
num = int(np.log2(len(rho)))
bloch_data = []
for i in range(num):
pauli_singles = [
Pauli.pauli_single(num, i, 'X'),
Pauli.pauli_single(num, i, 'Y'),
Pauli.pauli_single(num, i, 'Z')
]
bloch_state = list(
map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles))
bloch_data.append(bloch_state)
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'data': bloch_data,
'divNumber': div_number,
'options': options
})
display(HTML(html + javascript))
def plot_state(quantum_state, method='city', filename=None, show=False):
"""Plot the quantum state.
Args:
quantum_state (ndarray): statevector or density matrix
representation of a quantum state.
method (str): Plotting method to use.
filename (str): the output file to save the plot as. If specified it
will save and exit and not open up the plot in a new window. If
`bloch` method is used a `-n` will be added to the filename before
the extension for each qubit.
show (bool): If set to true the rendered image will open in a new
window
Returns:
matplotlib.Figure: The matplotlib.Figure of the visualization
Raises:
VisualizationError: if the input is not a statevector or density
matrix, or if the state is not an multi-qubit quantum state.
"""
# Check if input is a statevector, and convert to density matrix
rho = np.array(quantum_state)
if rho.ndim == 1:
rho = np.outer(rho, np.conj(rho))
# Check the shape of the input is a square matrix
shape = np.shape(rho)
if len(shape) != 2 or shape[0] != shape[1]:
raise VisualizationError("Input is not a valid quantum state.")
# Check state is an n-qubit state
num = int(np.log2(len(rho)))
if 2**num != len(rho):
raise VisualizationError("Input is not a multi-qubit quantum state.")
fig = None
if method == 'city':
fig = plot_state_city(rho, filename=filename, show=show)
elif method == "paulivec":
fig = plot_state_paulivec(rho, filename=filename, show=show)
elif method == "qsphere":
fig = plot_state_qsphere(rho, filename=filename, show=show)
elif method == "bloch":
aspect = float(1 / num)
fig = plt.figure(figsize=plt.figaspect(aspect))
for i in range(num):
ax = fig.add_subplot(1, num, i + 1, projection='3d')
pauli_singles = [
Pauli.pauli_single(num, i, 'X'),
Pauli.pauli_single(num, i, 'Y'),
Pauli.pauli_single(num, i, 'Z')
]
bloch_state = list(
map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles))
plot_bloch_vector(bloch_state, "qubit " + str(i), ax=ax)
if filename:
plt.savefig(filename)
elif show:
plt.show()
elif method == "wigner":
fig = plot_wigner_function(rho, filename=filename, show=show)
elif method == "hinton":
fig = plot_hinton(rho, filename=filename, show=show)
return fig
