fix some docs

Author: refraction-ray

docs/source/advance.rst

@@ -5,7 +5,9 @@ Advanced Usage
 MPS Simulator
 ----------------
 
-Very straightforward to use, we provide the same set of API for ``MPSCircuit`` as ``Circuit``, 
+TensorCircuit-NG provides Matrix Product State (MPS) simulation as an efficient alternative to exact simulation for quantum circuits. MPS simulation can handle larger quantum systems by trading off accuracy for computational efficiency.
+
+MPS simulator is very straightforward to use, we provide the same set of API for ``MPSCircuit`` as ``Circuit``, 
 the only new line is to set the bond dimension for the new simulator.
 
 .. code-block:: python
@@ -70,7 +72,7 @@ Split Two-qubit Gates
 
 The two-qubit gates applied on the circuit can be decomposed via SVD, which may further improve the optimality of the contraction pathfinding.
 
-`split` configuration can be set at circuit-level or gate-level.
+``split`` configuration can be set at circuit-level or gate-level.
 
 .. code-block:: python
 
@@ -153,7 +155,7 @@ Jitted Function Save/Load
 
 To reuse the jitted function, we can save it on the disk via support from the TensorFlow `SavedModel <https://www.tensorflow.org/guide/saved_model>`_. That is to say, only jitted quantum function on the TensorFlow backend can be saved on the disk. 
 
-We wrap the tf-backend `SavedModel` as very easy-to-use function :py:meth:`tensorcircuit.keras.save_func` and :py:meth:`tensorcircuit.keras.load_func`.
+We wrap the tf-backend ``SavedModel`` as very easy-to-use function :py:meth:`tensorcircuit.keras.save_func` and :py:meth:`tensorcircuit.keras.load_func`.
 
 For the JAX-backend quantum function, one can first transform them into the tf-backend function via JAX experimental support: `jax2tf <https://github.com/google/jax/tree/main/jax/experimental/jax2tf>`_.
 

docs/source/sharpbits.rst

@@ -236,8 +236,8 @@ Vmap (vectorized map) outside a grad-like function may cause incorrected results
 Grad over vmap function
 ~~~~~~~~~~~~~~~~~~~~~~~~~
 
-A related issue is the different behavior for `K.grad(K.vmap(f))` on different backends. For tensorflow backend, the function to be differentiated has a scalar output which is the sum of all outputs.
+A related issue is the different behavior for ``K.grad(K.vmap(f))`` on different backends. For tensorflow backend, the function to be differentiated has a scalar output which is the sum of all outputs.
 
 However, for Jax backend, the function simply raise error as only scalar output function can be differentiated, no implicit sum of the vectorized ``f`` is assumed. For non-scalar output, one should use `jacrev` or `jacfwd` to get the gradient information.
 
-Specifically, `K.grad(K.vmap(f))` on TensorFlow backend is equilvalent to `K.grad(K.append(K.vamp(f), K.sum))` on Jax backend.
+Specifically, ``K.grad(K.vmap(f))`` on TensorFlow backend is equilvalent to ``K.grad(K.append(K.vamp(f), K.sum))`` on Jax backend.