qutree package#

Plot sets of multiqubit quantum pure states as a binary tree of Bloch spheres.

class qutree.BBT(num_qubits)[source]#

Bases: object

Class containing the data to plot the Bloch Binary Tree.

Parameters:

num_qubits (int) – number of qubits

add_data(states, colors=None, cmap='jet')[source]#

Add data of states to the tree computing the Bloch spheres parameters.

Parameters:

  • states (ndarray) – complex array of M samples

  • colors (Optional[ndarray]) – complex array of either Mx4 for already generated colors, M for values between 0 and 1 that will follow the colormap, by default it will be the indexes.

  • cmap (str) – string name of a matplotlib colormap (default : ‘jet’)

Return type:

None

plot_tree(azim=-40.0, elev=30.0, size_sphere=2.0, dst_file='')[source]#

Display the binary tree.

Parameters:

  • azim (float) – viewing angle -> azimuth (default:-40)

  • elev (float) – viewing angle -> elevation (default:30)

  • size_sphere (float) – size of each single sphere.

  • dst_file (Union[Path, str]) – name of the destination file, leave blank to not save the plot.

Return type:

None

qutree.bloch_points(xp, yp, zp, colors, ax=None, azim=-40.0, elev=30.0)[source]#

Plot points on a bloch spere.

Parameters:

  • xp (ndarray) – array of the x axis coordinate

  • yp (ndarray) – array of the y axis coordinate

  • zp (ndarray) – array of the z axis coordinate

  • colors – array of colors for each point

  • ax (Optional[Axes]) – ax where the Bloch Sphere will be plotted, if None one is created

  • azim (float) – azimuth to plot the sphere

  • elev (float) – azimuth to plot the sphere

Return type:

None

qutree.fun_recursive(psi, coord='', tree_vals=[], tree_idxs=[], tol=0.0001)[source]#

Recursive function going down the hilbert schmidt decomposition.

Parameters:

  • psi (ndarray) – array representing the state in the current subspace \((2^N,M)\)

  • coord (str) – string representing the current coordinate in the binary tree

  • tree_vals (list) – register storing the \(\theta\) and \(\phi\) of the Bloch sphere at each coordinate

  • tree_idxs (list) – register storing the coordinates

  • tol (Optional[float]) – tolerance to delete a subspace.

Returns:

  • phip – the global phases of the local subspace

  • n – the amplitude of the local subspace

  • tree_vals – register storing the \(\theta\) and \(\phi\) of the Bloch sphere at each coordinate

  • tree_idxs – register storing the coordinates

Return type:

Tuple[ndarray, ndarray, list, list]

qutree.nphi_psi(psi)[source]#

Decompose an array of complex into absolute value and angles.

Parameters:

psi (ndarray) – array of complex values

Returns:

  • r – array of absolute values

  • phi – array of angles from \([0, 2\pi]\)

Return type:

Tuple[ndarray, ndarray]

qutree.nthe_n0n1(n0, n1)[source]#

Carthesian to Polar.

Compute \(n\) and \(\theta\) such that \([n0,n1] = n[cos(\theta),sin(\theta)]\)

Parameters:

  • n0 (ndarray) – array of absolute values

  • n1 (ndarray) – array of absolute values

Returns:

  • n – array of norm

  • the – array of angles from \([0, \pi]\)

Return type:

Tuple[ndarray, ndarray]

qutree.phimp_phi01(phi0, phi1)[source]#

Go from two subspace phases to local and global phase.

Parameters:

  • phi0 – array of subspace 0 phases

  • phi1 – array of subspace 1 phases

Returns:

  • phig – array of global phases

  • phil – array of local phases

qutree.thephi_to_xyz(the, phi)[source]#

Spherical to carthesian.

Parameters:

  • the (ndarray) – array of the angles \([0,\pi]\)

  • phi (ndarray) – array of \(\phi\) angles \([0,2 \pi]\)

Returns:

  • x – array of the x axis coordinate

  • y – array of the y axis coordinate

  • z – array of the z axis coordinate

Return type:

Tuple[ndarray, ndarray, ndarray]