update docs

Author: refraction-ray

docs/source/index.rst

@@ -7,6 +7,7 @@ TensorCircuit Next Generation
 
 **Welcome and congratulations! You have found TensorCircuit: the Next Generation.** 👏 
 
+
 Introduction
 ---------------
 
@@ -22,9 +23,11 @@ TensorCircuit-NG is an open-source high-performance quantum computing software f
 
 * It is implemented with industry-standard machine learning frameworks: TensorFlow, JAX, and PyTorch. 🤖
 
+* It is flexible and powerful to build and simulate tensor networks, neural networks and quantum circuits together. 🧠
+
 * It is compatible with machine learning engineering paradigms: automatic differentiation, just-in-time compilation, vectorized parallelism and GPU acceleration. 🛠
 
-With the help of TensorCircuit-NG, now get ready to efficiently and elegantly solve interesting and challenging quantum computing problems: from academic research prototype to industry application deployment.
+With the help of TensorCircuit-NG, now get ready to efficiently and elegantly solve interesting and challenging quantum computing and quantum many-body problems: from academic research prototype to industry application deployment.
 
 
 
@@ -153,19 +156,19 @@ TensorCircuit-NG is unifying infrastructures and interfaces for quantum computin
       :columns: 12 6 3 3
       :shadow: md
 
-      ideal/noisy/approximate simulation
+      ideal/noisy/approximate/analog simulation
 
    .. grid-item-card:: Unified Representations
       :columns: 12 6 3 3
       :shadow: md
 
       from/to_IR/qiskit/openqasm/json
 
-   .. grid-item-card:: Unified Pipelines
+   .. grid-item-card:: Unified Objects
       :columns: 12 6 3 3
       :shadow: md
 
-      stateless functional programming/stateful ML models
+      neural network/tensor network/quantum circuit
 
 
 

docs/source/quickstart.rst

@@ -15,7 +15,7 @@ Either pip from conda or other python env managers is fine.
 Since there are many optional packages for various features, 
 the users may need to install more pip packages when required. 
 
-- For Linux with Nvidia GPU,
+For Nvidia GPU,
 please refer to the GPU aware installation guide of corresponding machine learning frameworks: 
 `TensorFlow <https://www.tensorflow.org/install/gpu>`_, 
 `Jax <https://github.com/google/jax#pip-installation-gpu-cuda>`_, 
@@ -27,7 +27,6 @@ Docker is also recommended (especially Linux + Nvidia GPU setup):
 
 For more details on docker setup, please refer to `docker readme <https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/docker>`_.
 
-- For Windows, due to the lack of support for Jax, we recommend to use docker or WSL, please refer to `TC via windows docker <contribs/development_windows.html>`_ or `TC via WSL <contribs/development_wsl2.html>`_.
 
 Overall, the installation of TensorCircuit-NG is simple, since it is purely in Python and hence very portable. 
 As long as the users can take care of the installation of ML frameworks on the corresponding system, TensorCircuit-NG will work as expected.
@@ -239,6 +238,7 @@ To learn more about the jit mechanism, one can refer to documentation or blogs o
 
 Inputs, parameters, measurements, circuit structures, and Monte Carlo noise can all be evaluated in parallel.
 To learn more about vmap mechanism, one can refer to documentation or blogs on ``tf.vectorized_map`` or ``jax.vmap``.
+One can also refer to `tutorial <https://tensorcircuit-ng.readthedocs.io/en/latest/whitepaper/6-3-vmap.html>`_ for more details on the vmap usage in TensorCircuit-NG.
 
 
 Backend Agnosticism