示例#1
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def unitarity(oper):
    """
    Returns the unitarity of a quantum map, defined as the Frobenius norm
    of the unital block of that map's superoperator representation.

    Parameters
    ----------
    oper : Qobj
        Quantum map under consideration.

    Returns
    -------
    u : float
        Unitarity of ``oper``.
    """
    Eu = _super_to_superpauli(oper).full()[1:, 1:]
    #return np.real(np.trace(np.dot(Eu, Eu.conj().T))) / len(Eu)
    return np.linalg.norm(Eu, 'fro')**2 / len(Eu)
示例#2
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def unitarity(oper):
    """
    Returns the unitarity of a quantum map, defined as the Frobenius norm
    of the unital block of that map's superoperator representation.

    Parameters
    ----------
    oper : Qobj
        Quantum map under consideration.

    Returns
    -------
    u : float
        Unitarity of ``oper``.
    """
    Eu = _super_to_superpauli(oper).full()[1:, 1:]
    #return np.real(np.trace(np.dot(Eu, Eu.conj().T))) / len(Eu)
    return np.linalg.norm(Eu, 'fro')**2 / len(Eu)
示例#3
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def hinton(rho, xlabels=None, ylabels=None, title=None, ax=None, cmap=None,
           label_top=True):
    """Draws a Hinton diagram for visualizing a density matrix or superoperator.

    Parameters
    ----------
    rho : qobj
        Input density matrix or superoperator.

    xlabels : list of strings or False
        list of x labels

    ylabels : list of strings or False
        list of y labels

    title : string
        title of the plot (optional)

    ax : a matplotlib axes instance
        The axes context in which the plot will be drawn.

    cmap : a matplotlib colormap instance
        Color map to use when plotting.

    label_top : bool
        If True, x-axis labels will be placed on top, otherwise
        they will appear below the plot.

    Returns
    -------
    fig, ax : tuple
        A tuple of the matplotlib figure and axes instances used to produce
        the figure.

    Raises
    ------
    ValueError
        Input argument is not a quantum object.

    """

    # Apply default colormaps.
    # TODO: abstract this away into something that makes default
    #       colormaps.
    cmap = (
        (cm.Greys_r if settings.colorblind_safe else cm.RdBu)
        if cmap is None else cmap
    )

    # Extract plotting data W from the input.
    if isinstance(rho, Qobj):
        if rho.isoper:
            W = rho.full()

            # Create default labels if none are given.
            if xlabels is None or ylabels is None:
                labels = _cb_labels(rho.dims[0])
                xlabels = xlabels if xlabels is not None else list(labels[0])
                ylabels = ylabels if ylabels is not None else list(labels[1])

        elif rho.isoperket:
            W = vector_to_operator(rho).full()
        elif rho.isoperbra:
            W = vector_to_operator(rho.dag()).full()
        elif rho.issuper:
            if not _isqubitdims(rho.dims):
                raise ValueError("Hinton plots of superoperators are "
                                 "currently only supported for qubits.")
            # Convert to a superoperator in the Pauli basis,
            # so that all the elements are real.
            sqobj = _super_to_superpauli(rho)
            nq = int(log2(sqobj.shape[0]) / 2)
            W = sqobj.full().T
            # Create default labels, too.
            if (xlabels is None) or (ylabels is None):
                labels = list(map("".join, it.product("IXYZ", repeat=nq)))
                xlabels = xlabels if xlabels is not None else labels
                ylabels = ylabels if ylabels is not None else labels

        else:
            raise ValueError(
                "Input quantum object must be an operator or superoperator."
            )

    else:
        W = rho

    if ax is None:
        fig, ax = plt.subplots(1, 1, figsize=(8, 6))
    else:
        fig = None

    if not (xlabels or ylabels):
        ax.axis('off')

    ax.axis('equal')
    ax.set_frame_on(False)

    height, width = W.shape

    w_max = 1.25 * max(abs(np.diag(np.matrix(W))))
    if w_max <= 0.0:
        w_max = 1.0

    ax.fill(array([0, width, width, 0]), array([0, 0, height, height]),
            color=cmap(128))
    for x in range(width):
        for y in range(height):
            _x = x + 1
            _y = y + 1
            if np.real(W[x, y]) > 0.0:
                _blob(_x - 0.5, height - _y + 0.5, abs(W[x,
                      y]), w_max, min(1, abs(W[x, y]) / w_max), cmap=cmap)
            else:
                _blob(_x - 0.5, height - _y + 0.5, -abs(W[
                      x, y]), w_max, min(1, abs(W[x, y]) / w_max), cmap=cmap)

    # color axis
    norm = mpl.colors.Normalize(-abs(W).max(), abs(W).max())
    cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
    mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)

    # x axis
    ax.xaxis.set_major_locator(plt.IndexLocator(1, 0.5))

    if xlabels:
        ax.set_xticklabels(xlabels)
        if label_top:
            ax.xaxis.tick_top()
    ax.tick_params(axis='x', labelsize=14)

    # y axis
    ax.yaxis.set_major_locator(plt.IndexLocator(1, 0.5))
    if ylabels:
        ax.set_yticklabels(list(reversed(ylabels)))
    ax.tick_params(axis='y', labelsize=14)

    return fig, ax
示例#4
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def hinton(rho,
           xlabels=None,
           ylabels=None,
           title=None,
           ax=None,
           cmap=None,
           label_top=True):
    """Draws a Hinton diagram for visualizing a density matrix or superoperator.

    Parameters
    ----------
    rho : qobj
        Input density matrix or superoperator.

    xlabels : list of strings or False
        list of x labels

    ylabels : list of strings or False
        list of y labels

    title : string
        title of the plot (optional)

    ax : a matplotlib axes instance
        The axes context in which the plot will be drawn.

    cmap : a matplotlib colormap instance
        Color map to use when plotting.

    label_top : bool
        If True, x-axis labels will be placed on top, otherwise
        they will appear below the plot.

    Returns
    -------
    fig, ax : tuple
        A tuple of the matplotlib figure and axes instances used to produce
        the figure.

    Raises
    ------
    ValueError
        Input argument is not a quantum object.

    """

    # Apply default colormaps.
    # TODO: abstract this away into something that makes default
    #       colormaps.
    cmap = ((cm.Greys_r if settings.colorblind_safe else cm.RdBu)
            if cmap is None else cmap)

    # Extract plotting data W from the input.
    if isinstance(rho, Qobj):
        if rho.isoper:
            W = rho.full()

            # Create default labels if none are given.
            if xlabels is None or ylabels is None:
                labels = _cb_labels(rho.dims[0])
                xlabels = xlabels if xlabels is not None else list(labels[0])
                ylabels = ylabels if ylabels is not None else list(labels[1])

        elif rho.isoperket:
            W = vector_to_operator(rho).full()
        elif rho.isoperbra:
            W = vector_to_operator(rho.dag()).full()
        elif rho.issuper:
            if not _isqubitdims(rho.dims):
                raise ValueError("Hinton plots of superoperators are "
                                 "currently only supported for qubits.")
            # Convert to a superoperator in the Pauli basis,
            # so that all the elements are real.
            sqobj = _super_to_superpauli(rho)
            nq = int(log2(sqobj.shape[0]) / 2)
            W = sqobj.full().T
            # Create default labels, too.
            if (xlabels is None) or (ylabels is None):
                labels = list(map("".join, it.product("IXYZ", repeat=nq)))
                xlabels = xlabels if xlabels is not None else labels
                ylabels = ylabels if ylabels is not None else labels

        else:
            raise ValueError(
                "Input quantum object must be an operator or superoperator.")

    else:
        W = rho

    if ax is None:
        fig, ax = plt.subplots(1, 1, figsize=(8, 6))
    else:
        fig = None

    if not (xlabels or ylabels):
        ax.axis('off')

    ax.axis('equal')
    ax.set_frame_on(False)

    height, width = W.shape

    w_max = 1.25 * max(abs(np.diag(np.matrix(W))))
    if w_max <= 0.0:
        w_max = 1.0

    ax.fill(array([0, width, width, 0]),
            array([0, 0, height, height]),
            color=cmap(128))
    for x in range(width):
        for y in range(height):
            _x = x + 1
            _y = y + 1
            if np.real(W[x, y]) > 0.0:
                _blob(_x - 0.5,
                      height - _y + 0.5,
                      abs(W[x, y]),
                      w_max,
                      min(1,
                          abs(W[x, y]) / w_max),
                      cmap=cmap)
            else:
                _blob(_x - 0.5,
                      height - _y + 0.5,
                      -abs(W[x, y]),
                      w_max,
                      min(1,
                          abs(W[x, y]) / w_max),
                      cmap=cmap)

    # color axis
    norm = mpl.colors.Normalize(-abs(W).max(), abs(W).max())
    cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
    mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)

    # x axis
    ax.xaxis.set_major_locator(plt.IndexLocator(1, 0.5))

    if xlabels:
        ax.set_xticklabels(xlabels)
        if label_top:
            ax.xaxis.tick_top()
    ax.tick_params(axis='x', labelsize=14)

    # y axis
    ax.yaxis.set_major_locator(plt.IndexLocator(1, 0.5))
    if ylabels:
        ax.set_yticklabels(list(reversed(ylabels)))
    ax.tick_params(axis='y', labelsize=14)

    return fig, ax