update readme

Author: refraction-ray

README.md

@@ -25,17 +25,17 @@
 
 <p align="center"> English | <a href="README_cn.md"> 简体中文 </a></p>
 
-TensorCircuit-NG is the next-generation open-source high-performance quantum software framework, built upon tensornetwork engines, supporting for automatic differentiation, just-in-time compiling, hardware acceleration, and vectorized parallelism, providing unified infrastructures and interfaces for quantum programming. It can compose quantum circuits, neural networks and tensor networks seamlessly with high simulation efficiency and flexibility.
+TensorCircuit-NG is the next-generation open-source high-performance quantum software framework, built upon tensornetwork engines, supporting for automatic differentiation, just-in-time compiling, hardware acceleration, vectorized parallelism and distributed training, providing unified infrastructures and interfaces for quantum programming. It can compose quantum circuits, neural networks and tensor networks seamlessly with high simulation efficiency and flexibility.
 
-TensorCircuit-NG is built on top of modern machine learning frameworks: Jax, TensorFlow, and PyTorch. It is specifically suitable for large-scale simulations of quantum-classical hybrid paradigm and variational quantum algorithms in ideal, noisy, Clifford, approximate and analog cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.
+TensorCircuit-NG is built on top of modern machine learning frameworks: Jax, TensorFlow, and PyTorch. It is specifically suitable for large-scale simulations of quantum-classical hybrid paradigm and variational quantum algorithms in ideal, noisy, Clifford, approximate, analog and fermionic cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.
 
-TensorCircuit-NG is the actively maintained official version and a [fully compatible](https://tensorcircuit-ng.readthedocs.io/en/latest/faq.html#what-is-the-relation-between-tensorcircuit-and-tensorcircuit-ng) successor to TensorCircuit with more new features (stabilizer circuit and distributed simulation) and bug fixes (support latest `numpy>2` and `qiskit>1`).
+TensorCircuit-NG is the actively maintained official version and a [fully compatible](https://tensorcircuit-ng.readthedocs.io/en/latest/faq.html#what-is-the-relation-between-tensorcircuit-and-tensorcircuit-ng) successor to TensorCircuit with more new features (stabilizer circuit, multi-card distributed simulation, etc.) and bug fixes (support latest `numpy>2` and `qiskit>1`).
 
 ## Getting Started
 
 Please begin with [Quick Start](/docs/source/quickstart.rst) in the [full documentation](https://tensorcircuit-ng.readthedocs.io/).
 
-For more information on software usage, sota algorithm implementation and engineer paradigm demonstration, please refer to 80+ [example scripts](/examples) and 30+ [tutorial notebooks](https://tensorcircuit-ng.readthedocs.io/en/latest/#tutorials). API docstrings and test cases in [tests](/tests) are also informative. One can also refer to tensorcircuit-ng [deepwiki](https://deepwiki.com/tensorcircuit/tensorcircuit-ng) generated by LLM.
+For more information on software usage, sota algorithm implementation and engineer paradigm demonstration, please refer to 80+ [example scripts](/examples) and 30+ [tutorial notebooks](https://tensorcircuit-ng.readthedocs.io/en/latest/#tutorials). API docstrings and test cases in [tests](/tests) are also informative. One can also refer to tensorcircuit-ng [deepwiki](https://deepwiki.com/tensorcircuit/tensorcircuit-ng) by LLM.
 
 For beginners, please refer to [quantum computing lectures with TC-NG](https://github.com/sxzgroup/qc_lecture) to learn both quantum computing basics and representative usage of TensorCircuit-NG.
 
@@ -135,7 +135,7 @@ The package is written in pure Python and can be obtained via pip as:
 pip install tensorcircuit-ng
 ```
 
-We recommend you install this package with tensorflow also installed as:
+We recommend you install this package with tensorflow or jax also installed as:
 
 ```python
 pip install "tensorcircuit-ng[tensorflow]"

examples/distributed_interface_vqe.py

@@ -112,7 +112,6 @@ def opt_update(params, opt_state, grads):
         print(f"Step {i+1:03d} | " f"Loss: {loss:.8f} | " f"Time: {t1 - t0:.4f} s")
 
     print("\nOptimization finished.")
-    final_energy = DC.value(
-        params, op=lambda x: K.real(K.sum(x)), output_dtype=tc.rdtypestr
-    )
+    real = lambda x: K.real(K.sum(x))
+    final_energy = DC.value(params, op=real, output_dtype=tc.rdtypestr)
     print(f"Final energy: {final_energy:.8f}")

tensorcircuit/experimental.py

@@ -901,6 +901,7 @@ def value_and_grad(
         :param aggregate: Whether to aggregate (sum) the results across devices, defaults to True
         :type aggregate: bool, optional
         :param op: Optional post-processing function for the output, defaults to None (corresponding to `backend.real`)
+            op is a cache key, so dont directly pass lambda function for op
         :type op: Optional[Callable[[Tensor], Tensor]], optional
         :param output_dtype: dtype str for the output of `nodes_fn`, defaults to None (corresponding to `rdtypestr`)
         :type output_dtype: Optional[str], optional
@@ -939,6 +940,7 @@ def value(
         :param aggregate: Whether to aggregate (sum) the results across devices, defaults to True
         :type aggregate: bool, optional
         :param op: Optional post-processing function for the output, defaults to None (corresponding to identity)
+            op is a cache key, so dont directly pass lambda function for op
         :type op: Optional[Callable[[Tensor], Tensor]], optional
         :param output_dtype: dtype str for the output of `nodes_fn`, defaults to None (corresponding to `dtypestr`)
         :type output_dtype: Optional[str], optional