From a44dc447e459a8c001d004353187c1acb0138892 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Elena=20Pe=C3=B1a=20Tapia?= <epenatap@gmail.com>
Date: Wed, 21 Feb 2024 17:08:51 +0100
Subject: [PATCH 1/3] Add conventions to readme

---
 README.md | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)

diff --git a/README.md b/README.md
index a0540f7..3680b10 100644
--- a/README.md
+++ b/README.md
@@ -43,6 +43,36 @@ can be applied to best run quantum optimization algorithms on real hardware:
 3. Application of SWAP strategies -> `swap_strategies`
 4. QAOA cost function -> `cost_function`
 
+## Notation Conventions
+
+The convention in this repository is that the (depth-one) QAOA should create an Ansatz of the form:
+
+$$
+\begin{align}
+\exp\left(-i\beta H_m\right)\exp\left(-i\gamma H_c\right)\vert+\rangle^{\otimes n}
+\end{align}
+$$
+
+to **minimize** the energy of $H_c$. Since we are minimizing $\\langle H_c\\rangle$, 
+the initial state of the ansatz should be the ground state of the mixer $H_m$. This enforces:
+
+$$
+\\begin{align}
+H_m=-\\sum_iX_i.
+\\end{align}
+$$
+
+As cost operator we apply:
+
+$$
+\\begin{align}
+H_c=\\sum_{i,j=0}^{n-1}w_{i,j}Z_iZ_j
+\\end{align}
+$$
+
+At the circuit level, these definitions imply that the exponential of the mixer is built 
+with $R_x(-2\\beta)$ rotations and the exponential of the cost operator is built from $R_{zz}(2\\gamma w_{i,j})$.
+
 
 ## References
 1. Sack, S. H., & Egger, D. J. (2023). Large-scale quantum approximate optimization on non-planar graphs with machine learning noise mitigation. arXiv preprint arXiv:2307.14427. [Link](https://arxiv.org/pdf/2307.14427.pdf).

From ac0aea02572f7726df917e9591b26660d7ddf115 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Elena=20Pe=C3=B1a=20Tapia?= <epenatap@gmail.com>
Date: Wed, 21 Feb 2024 17:13:23 +0100
Subject: [PATCH 2/3] Modify title

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3680b10..b096140 100644
--- a/README.md
+++ b/README.md
@@ -43,7 +43,7 @@ can be applied to best run quantum optimization algorithms on real hardware:
 3. Application of SWAP strategies -> `swap_strategies`
 4. QAOA cost function -> `cost_function`
 
-## Notation Conventions
+## QAOA Formulation Convention
 
 The convention in this repository is that the (depth-one) QAOA should create an Ansatz of the form:
 

From 326f1df1656865ce62360f1424e1e70908d9f692 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Elena=20Pe=C3=B1a=20Tapia?= <epenatap@gmail.com>
Date: Thu, 22 Feb 2024 09:24:52 +0100
Subject: [PATCH 3/3] Apply Daniel's feedback

---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index b096140..375ae96 100644
--- a/README.md
+++ b/README.md
@@ -70,6 +70,8 @@ H_c=\\sum_{i,j=0}^{n-1}w_{i,j}Z_iZ_j
 \\end{align}
 $$
 
+where the sum runs over $i<j$.
+
 At the circuit level, these definitions imply that the exponential of the mixer is built 
 with $R_x(-2\\beta)$ rotations and the exponential of the cost operator is built from $R_{zz}(2\\gamma w_{i,j})$.