Implement Bloch Sphere rendering

CHANGELOG.md

@@ -9,6 +9,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 - Introduce `Lanczos` solver for `spectrum`. ([#476])
 - Add Bloch-Redfield master equation solver. ([#473])
+- Implement Bloch Sphere rendering. ([#472])
 
 ## [v0.31.1]
 Release date: 2025-05-16
@@ -231,5 +232,6 @@ Release date: 2024-11-13
 [#455]: https://github.com/qutip/QuantumToolbox.jl/issues/455
 [#456]: https://github.com/qutip/QuantumToolbox.jl/issues/456
 [#460]: https://github.com/qutip/QuantumToolbox.jl/issues/460
+[#472]: https://github.com/qutip/QuantumToolbox.jl/issues/472
 [#473]: https://github.com/qutip/QuantumToolbox.jl/issues/473
 [#476]: https://github.com/qutip/QuantumToolbox.jl/issues/476

docs/make.jl

@@ -51,6 +51,7 @@ const PAGES = [
         ],
         "Manipulating States and Operators" => "users_guide/states_and_operators.md",
         "Tensor Products and Partial Traces" => "users_guide/tensor.md",
+        "Plotting on the Bloch Sphere" => "users_guide/plotting_the_bloch_sphere.md",
         "Time Evolution and Dynamics" => [
             "Introduction" => "users_guide/time_evolution/intro.md",
             "Time Evolution Solutions" => "users_guide/time_evolution/solution.md",

docs/src/resources/api.md

@@ -319,4 +319,13 @@ meshgrid
 ```@docs
 plot_wigner
 plot_fock_distribution
+plot_bloch
+Bloch
+render
+add_points!
+add_vectors!
+add_line!
+add_arc!
+clear!
+add_states!
 ```

docs/src/users_guide/extensions/cairomakie.md

@@ -19,4 +19,5 @@ The supported plotting functions are listed as follows:
 | **Plotting Function** | **Description** |
 |:----------------------|:----------------|
 | [`plot_wigner`](@ref) | [Wigner quasipropability distribution](https://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution) |
-| [`plot_fock_distribution`](@ref) | [Fock state](https://en.wikipedia.org/wiki/Fock_state) distribution |
+| [`plot_fock_distribution`](@ref) | [Fock state](https://en.wikipedia.org/wiki/Fock_state) distribution |
+| [`plot_bloch`](@ref)  | [Plotting on the Bloch Sphere](@ref doc:Plotting-on-the-Bloch-Sphere) |

docs/src/users_guide/plotting_the_bloch_sphere.md

@@ -0,0 +1,160 @@
+# [Plotting on the Bloch Sphere](@id doc:Plotting-on-the-Bloch-Sphere)
+
+```@setup Bloch_sphere_rendering
+using QuantumToolbox
+
+using CairoMakie
+CairoMakie.enable_only_mime!(MIME"image/svg+xml"())
+```
+
+## [Introduction](@id doc:Bloch_sphere_rendering)
+
+When studying the dynamics of a two-level system, it's often convenient to visualize the state of the system by plotting the state vector or density matrix on the Bloch sphere.
+
+In [QuantumToolbox.jl](https://qutip.org/QuantumToolbox.jl/), this can be done using the [`Bloch`](@ref) or [`plot_bloch`](@ref) methods that provide same syntax as [QuTiP](https://qutip.readthedocs.io/en/stable/guide/guide-bloch.html).
+
+## Create a Bloch Sphere
+
+In [QuantumToolbox.jl](https://qutip.org/QuantumToolbox.jl/), creating a [`Bloch`](@ref) sphere is accomplished by calling either:
+
+```@example Bloch_sphere_rendering
+b = Bloch();
+```
+
+which will load an instance of [`Bloch`](@ref). Before getting into the details of these objects, we can simply plot the blank [`Bloch`](@ref) sphere associated with these instances via:
+
+```@example Bloch_sphere_rendering
+fig, _ = render(b);
+fig
+```
+
+## Add a Single Data Point
+
+As an example, we can add a single data point via [`add_points!`](@ref):
+
+```@example Bloch_sphere_rendering
+pnt = [1 / sqrt(3), 1 / sqrt(3), 1 / sqrt(3)];
+add_points!(b, pnt);
+fig, _ = render(b);
+fig
+```
+
+## Add a Single Vector
+
+and then a single vector via  [`add_vectors!`](@ref):
+
+```@example Bloch_sphere_rendering
+vec = [0, 1, 0];
+add_vectors!(b, vec)
+fig, _ = render(b)
+fig
+```
+
+and then add another vector corresponding to the ``|0\rangle`` state:
+
+```@example Bloch_sphere_rendering
+x = basis(2, 0)
+add_states!(b, [x])
+fig, _ = render(b)
+fig
+```
+
+## Add Multiple Vectors
+
+We can also plot multiple points, vectors, and states at the same time by passing arrays instead of individual elements via  [`add_vectors!](@ref). Before giving an example, we can use [`clear!`](@ref) to remove the current data from our [`Bloch`](@ref) sphere instead of creating a new instance:
+
+```@example Bloch_sphere_rendering
+clear!(b)
+fig, _ = render(b)
+fig
+```
+
+Now on the same [`Bloch`](@ref) sphere, we can plot the three states via [`add_states!`](@ref) associated with the `x`, `y`, and `z` directions:
+
+```@example Bloch_sphere_rendering
+x = basis(2, 0) + basis(2, 1)
+y = basis(2, 0) - im * basis(2, 1)
+z = basis(2, 0)
+b = Bloch()
+add_states!(b, [x, y, z])
+fig, _ = render(b)
+fig
+```
+
+A similar method works for adding vectors:
+
+```@example Bloch_sphere_rendering
+clear!(b)
+vecs = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
+add_vectors!(b, vecs)
+fig, _ = render(b)
+fig
+```
+
+# Add Arc, Line, and Vector
+
+You can also add lines and arcs via [`add_line!`](@ref) and [`add_arc!`](@ref) respectively:
+
+```@example Bloch_sphere_rendering
+clear!(b)
+vec = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
+add_vectors!(b, vec);
+add_line!(b, [1,0,0], [0,1,0])
+add_arc!(b, [1, 0, 0], [0, 1, 0], [0, 0, 1])
+fig, _ = render(b)
+fig
+```
+
+## Add Multiple Points
+
+Adding multiple points to the [`Bloch`](@ref) sphere works slightly differently than adding multiple states or vectors. For example, lets add a set of `20` points around the equator (after calling [`clear!`](@ref)):
+
+```@example Bloch_sphere_rendering
+th = range(0, 2π; length=20);
+clear!(b)
+xp = cos.(th);
+yp = sin.(th);
+zp = zeros(20);
+pnts = [xp, yp, zp];
+add_points!(b, pnts);
+fig, ax = render(b);
+fig
+```
+
+Notice that, in contrast to states or vectors, each point remains the same color as the initial point. This is because adding multiple data points using [`add_points!`](@ref) is interpreted, by default, to correspond to a single data point (single qubit state) plotted at different times. This is very useful when visualizing the dynamics of a qubit. If we want to plot additional qubit states we can call additional [`add_points!`](@ref):
+
+## Add Another Set of Points
+
+```@example Bloch_sphere_rendering
+xz = zeros(20);
+yz = sin.(th);
+zz = cos.(th);
+pnts = [xz, yz, zz];
+add_points!(b, pnts);
+fig, ax = render(b);
+fig
+```
+
+The color and shape of the data points is varied automatically by [`Bloch`](@ref). Notice how the color and point markers change for each set of data.
+
+What if we want to vary the color of our points. We can tell [`Bloch`](@ref) to vary the color of each point according to the colors listed in the `point_color` attribute.
+
+```@example Bloch_sphere_rendering
+clear!(b)
+xp = cos.(th);
+yp = sin.(th);
+zp = zeros(20);
+pnts = [xp, yp, zp];
+add_points!(b, pnts, meth=:m);
+fig, ax = render(b);
+fig
+```
+
+Now, the data points cycle through a variety of predefined colors. Now lets add another set of points, but this time we want the set to be a single color, representing say a qubit going from the ``|0\rangle`` state to the ``|1\rangle`` state in the `y-z` plane:
+
+```@example Bloch_sphere_rendering
+pnts = [xz, yz, zz] ;
+add_points!(b, pnts);
+fig, ax = render(b);
+fig
+```