Add Makefile command for starting Vitepress locally and some minor changes

Makefile

@@ -12,13 +12,18 @@ docs:
 	${JULIA} --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
 	${JULIA} --project=docs docs/make.jl
 
-all: format test docs
+vitepress:
+	npm --prefix docs i
+	npm --prefix docs run docs:dev
+
+all: format test docs vitepress
 
 help:
 	@echo "The following make commands are available:"
 	@echo " - make format: format codes with JuliaFormatter"
 	@echo " - make test: run the tests"
 	@echo " - make docs: instantiate and build the documentation"
+	@echo " - make vitepress: start Vitepress site of documentation"
 	@echo " - make all: run every commands in the above order"
 
-.PHONY: default format test docs all help
+.PHONY: default format test docs vitepress all help

README.md

@@ -65,7 +65,7 @@ QuantumToolbox.jl is equipped with a robust set of features:
 
 - **Quantum State and Operator Manipulation:** Easily handle quantum states and operators with a rich set of tools, with the same functionalities as QuTiP.
 - **Dynamical Evolution:** Advanced solvers for time evolution of quantum systems, thanks to the powerful [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl) package.
-- **GPU Computing:** Leverage GPU resources for high-performance computing. For example, you run the master equation directly on the GPU with the same syntax as the CPU case.
+- **GPU Computing:** Leverage GPU resources for high-performance computing. Simulate quantum dynamics directly on the GPU with the same syntax as the CPU case.
 - **Distributed Computing:** Distribute the computation over multiple nodes (e.g., a cluster). For example, you can run hundreds of quantum trajectories in parallel on a cluster, with, again, the same syntax as the simple case.
 - **Easy Extension:** Easily extend the package, taking advantage of the Julia language features, like multiple dispatch and metaprogramming.
 

docs/README.md

@@ -1,17 +1,24 @@
-# How to build documentation locally ?
+# How to build documentation and start Vitepress site locally ?
 
 ## Working Directory
 All the commands should be run under the root folder of the package: `/path/to/QuantumToolbox.jl/`
 
 The document pages will be generated in the directory: `/path/to/QuantumToolbox.jl/docs/build/` (which is ignored by git).
 
 ## Method 1: Run with `make` command
-Run the following command:
+Run the following command to instantiate and build the documentation:
 ```shell
 make docs
 ```
 
-## Method 2: Run `julia` command manually
+Run the following command to start Vitepress site of documentation:
+> [!NOTE]
+> You need to install `Node.js` and `npm` first.
+```shell
+make vitepress
+```
+
+## Method 2: Run commands manually
 
 ### Build Pkg
 Run the following command:
@@ -26,22 +33,16 @@ Run the following command:
 julia --project=docs docs/make.jl
 ```
 
-# How to start a local Vitepress site ?
-
+### Start a local Vitepress site
 > [!NOTE]
-> You need to install `Node.js` and `npm` first. 
-
-Enter `docs` directory first:
-```shell
-cd /path/to/QuantumToolbox.jl/docs
-```
+> You need to install `Node.js` and `npm` first.
 
 Install `npm` dependencies:
 ```shell
-npm i
+npm --prefix docs i
 ```
 
 Run the following command:
 ```shell
-npm run docs:dev
+npm --prefix docs run docs:dev
 ```

docs/src/index.md

@@ -5,7 +5,7 @@ layout: home
 
 hero:
   name: "QuantumToolbox.jl"
-  tagline: High-performance quantum simulations made simple
+  tagline: A pure Julia framework designed for High-performance quantum physics simulations
   image:
     src: /logo.png
     alt: QuantumToolbox
@@ -25,17 +25,21 @@ hero:
 
 
 features:
+  - icon: <img width="64" height="64" src="https://qutip.org/images/logo.png" alt="markdown"/>
+    title: QuTiP
+    details: Easily handle quantum states and operators with a rich set of tools, with the same functionalities as Python QuTiP.
+    link: https://qutip.org/
   - icon: <img width="64" height="64" src="https://docs.sciml.ai/DiffEqDocs/stable/assets/logo.png" alt="markdown"/>
     title: Dynamical Evolution
     details: Advanced solvers for time evolution of quantum systems, thanks to the powerful DifferentialEquations.jl package.
     link: /users_guide/time_evolution/intro
   - icon: <img width="64" height="64" src="https://cuda.juliagpu.org/stable/assets/logo.png" />
     title: GPU Computing
-    details: Leverage GPU resources for high-performance computing. Simulate the master equation directly on the GPU with the same syntax as the CPU case.
+    details: Leverage GPU resources for high-performance computing. Simulate quantum dynamics directly on the GPU with the same syntax as the CPU case.
     link: /getting_started
   - icon: <img width="64" height="64" src="https://img.icons8.com/?size=100&id=1W4Bkj363ov0&format=png&color=000000" />
     title: Distributed Computing
-    details: Distribute the computation over multiple nodes (e.g., a cluster). Simulate undreds of quantum trajectories in parallel on a cluster, with, again, the same syntax as the simple case.
+    details: Distribute the computation over multiple nodes (e.g., a cluster). Simulate hundreds of quantum trajectories in parallel on a cluster, with, again, the same syntax as the simple case.
     link: /users_guide/time_evolution/mcsolve
 ---
 ```