From e8c12906b7e3a6edaf0cce3adc47bf61c1cfd572 Mon Sep 17 00:00:00 2001
From: Thomas Watts <57363084+gingertonwatts@users.noreply.github.com>
Date: Thu, 5 Dec 2024 17:35:49 -0800
Subject: [PATCH] Update README.md

---
 Hamiltonian_features/README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Hamiltonian_features/README.md b/Hamiltonian_features/README.md
index ad5d6a4..915057a 100644
--- a/Hamiltonian_features/README.md
+++ b/Hamiltonian_features/README.md
@@ -23,9 +23,9 @@ Rank $L$
 
 Eigenvalues { $\lambda_\ell$ }
 
-Double factorization eigenvalue gap $|\lambda_1 - \lambda_2|$
+Double factorization eigenvalue gap $|\lambda_0 - \lambda_1|$
 
- $G(H) = (V,E)$ where $V = [n]$ for an $n$-qubit Hamiltonian $H$ where the edge set contains hyperedges $e_i = (i_1,...,i_{k(i)}) \in E$ where $i_1, ..., i_{k(i)} \in V$ are all those qubits that are being acted upon by non-identity single qubit Pauli operators. The graph has edge weights $w(e) = h_e$ where $h_e$ is the coefficient of Pauli string $e \in E$ where $H = \sum_{e \in E} h_e P_e$. We take statistics (max, min, mean, std. dev.) on edge order (Pauli weight), vertex degree, and edge weights.
+ $G(H) = (V,E)$ where $V = [n]$ for an $n$-qubit Hamiltonian $H$ where the edge set contains hyperedges $e = (i_1,...,i_{k(e)}) \in E$ where $i_1, ..., i_{k(e)} \in V$ are all those qubits that are being acted upon by non-identity single qubit Pauli operators; $k(e)$ is the number of these qubits for a given egde $e$. The graph has edge weights $h_e$ where $h_e$ is the coefficient of Pauli string $e \in E$ where $H = \sum_{e \in E} h_e P_e$. We take statistics (max, min, mean, std. dev.) on edge order (Pauli weight), vertex degree, and edge weights.
 
 One-norm
 
@@ -35,7 +35,7 @@ $$
 
 Number of Pauli Strings | $E$ |
 
-Edge Order $\mathrm{ord}(e_i) = k(i)$
+Edge Order $\mathrm{ord}(e) = k(e)$
 
 Vertex Degree $\mathrm{deg}(v)$ = |{ $e \in E : v \in e$ }|