diff --git a/mindq_projectq/benchmark/ADAPTVQE.md b/mindq_projectq/benchmark/ADAPTVQE.md
index 32442f5bd9b1992dc7bf9d11f0d7c1517f264b99..480b2d8555a58c6c9214761545f4a0dd7311ff84 100644
--- a/mindq_projectq/benchmark/ADAPTVQE.md
+++ b/mindq_projectq/benchmark/ADAPTVQE.md
@@ -10,15 +10,15 @@
 
 ​	The operator pool is constructed by operators in the UCCSD or UCCGSD ansatz.
 
-​	Spin complemented operators: 
+​	Spin complemented single and double operators: 
 
-​	for example: H2(4 spin orbital)
+​	For example: H2 (4 spin orbital)
 
-​	single operator: 
+​	single fermionic operator:
 
 ​	$-0.5\hat{a}_0^\dagger\hat{a}_2 + 	-0.5\hat{a}_1^\dagger\hat{a}_3 + 0.5\hat{a}_0^\dagger\hat{a}_2+0.5\hat{a}_3^\dagger\hat{a}_1$
 
-​	double operator:
+​	double fermionic operator:
 
 ​	$-\frac{1}{\sqrt{2}}\hat{a}_1^\dagger\hat{a}_0^\dagger\hat{a}_2\hat{a}_3+\frac{1}{\sqrt{2}}\hat{a}_3^\dagger\hat{a}_2^\dagger\hat{a}_1\hat{a}_0$
 
@@ -60,17 +60,25 @@
 
 8. Go to step 4.
 
-NOTE:
+
+
+## 4. Setting:
 
 1. The gradient of each operator in the pool can also be approximated by the parameter shift rule.
 
-   $\frac{\partial E^{(n)}}{\partial\theta_n}|_{\theta_n=0}\approx\frac{E^{(n)}(\vec{\theta}_{i-1}, \theta_n=\delta)-E^{(n)}(\vec{\theta}_{i-1}, \theta_n=-\delta)}{2\delta}$, where $E^{(n)}(\vec{\theta}_{i-1}, \theta_n=\delta)=\langle \psi^{(n-1)}|e^{-\delta\hat{A}_i}\hat{H}e^{\delta\hat{A}_i}|\psi^{(n-1)}\rangle$. ($\delta=1e-5$)
+   $\frac{\partial E^{(n)}}{\partial\theta_n}|_{\theta_n=0}\approx\frac{E^{(n)}(\vec{\theta}_{i-1}, \theta_n=\delta)-E^{(n)}(\vec{\theta}_{i-1}, \theta_n=-\delta)}{2\delta}$, where $E^{(n)}(\vec{\theta}{i-1}, \theta_n=\delta)=\langle \psi^{(n-1)}|e^{-\delta\hat{A}_i}\hat{H}e^{\delta\hat{A}_i}|\psi^{(n-1)}\rangle$ .
+
+   Here we set $\delta = 1e-5$ .
 
 2. The convergence condition is set as 
 
-   $\sqrt{\sum_{\hat{A}_i \in pool} \langle \psi^{(n-1)}|[\hat{H},\hat{A}_i]|\psi^{(n-1)}\rangle} \le \varepsilon$, and $\varepsilon = 1e-2$
+   $\sqrt{\sum_{\hat{A}_i \in pool} \langle \psi^{(n-1)}|[\hat{H},\hat{A}_i]|\psi^{(n-1)}\rangle} \le \varepsilon$, and $\varepsilon = 1e-2$ .
+
+3. Optimizer:
+
+   **BFGS**: Broyden–Fletcher–Goldfarb–Shanno algorithm. (tol=1e-6)
 
-## 4. Reference	
+## 5. Reference	
 
 ​	origin paper: [An adaptive variational algorithm for exact molecular simulations on a quantum computer](https://doi.org/10.1038/s41467-019-10988-2 | www.nature.com/naturecommunications)
 
diff --git a/mindq_projectq/benchmark/QCC.md b/mindq_projectq/benchmark/QCC.md
index 6b65a21f22497ef862e10b3702dbff79202fb65c..365ec8dce153e3cedb49587677461de9443d39d9 100644
--- a/mindq_projectq/benchmark/QCC.md
+++ b/mindq_projectq/benchmark/QCC.md
@@ -36,7 +36,11 @@ $$
 
 ​	The quantity of all entanglers is $4^{N_q}-3N_q-1$. A pre-screening based on the first and second terms of the Taylor expansion by evaluating $\frac{d E(\tau, \hat{P})}{d\tau} |_{\tau=0}$ and $\frac{d^2 E(\tau, \hat{P})}{d^2 \tau} |_{\tau=0}$.
 
-## 3. Reference
+## 3. Setting
+
+    This part will be added later.
+
+## 4. Reference
 
 origin paper: [Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer]([Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer | Journal of Chemical Theory and Computation (acs.org)](https://pubs.acs.org/doi/full/10.1021/acs.jctc.8b00932))
 
diff --git a/mindq_projectq/benchmark/qubit-ADAPT-VQE.md b/mindq_projectq/benchmark/qubit-ADAPT-VQE.md
index 107c9f37cc81e855cdcfe79583cab3bc34369e31..809dff236326682c628d7b1c28988be23d55e228 100644
--- a/mindq_projectq/benchmark/qubit-ADAPT-VQE.md
+++ b/mindq_projectq/benchmark/qubit-ADAPT-VQE.md
@@ -55,9 +55,14 @@
 
 
 
+**Note**: qubit-ADAPT-VQE is quite similar to ADAPT VQE except for the "qubit pool".
 
-**Note**: A convergence condition is not given in the original paper. Therefore,  a suitable one can be defined by yourself.
-## 4. Reference
+## 4. Setting
+
+   A convergence condition is not given in the original paper. Therefore, a suitable
+one can be defined by yourself.
+
+## 5. Reference
 
 ​	original paper: [Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ansätze on a Quantum Processor]([PRX Quantum 2, 020310 (2021) - Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ans\"atze on a Quantum Processor (aps.org)](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.020310))