Refactor README with improved content and structure

Updated README to enhance clarity and add abstract.

Author: sbryngelson

README.md

@@ -1,18 +1,14 @@
 ## Quantum HRF Tomography
 <img src="assets/logo-qht.png" alt="HRF Banner" width="300"/>
 
-[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](#license)
-<a href="https://github.com/comp-physics/Quantum-HRF-Tomography/actions">
-<img src="https://github.com/comp-physics/Quantum-HRF-Tomography/actions/workflows/ci.yml/badge.svg" />
-</a>
-[![Coverage Status](https://coveralls.io/repos/github/comp-physics/Quantum-HRF-Tomography/badge.svg)](https://coveralls.io/github/comp-physics/Quantum-HRF-Tomography)
-[![arXiv](https://img.shields.io/badge/arXiv-2505.06455-b31b1b.svg)](https://arxiv.org/abs/2505.06455)
+[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](#license) <a href="https://github.com/comp-physics/Quantum-HRF-Tomography/actions">
+<img src="https://github.com/comp-physics/Quantum-HRF-Tomography/actions/workflows/ci.yml/badge.svg" /> </a> [![Coverage Status](https://coveralls.io/repos/github/comp-physics/Quantum-HRF-Tomography/badge.svg)](https://coveralls.io/github/comp-physics/Quantum-HRF-Tomography) [![arXiv](https://img.shields.io/badge/arXiv-2505.06455-b31b1b.svg)](https://arxiv.org/abs/2505.06455)
 
 Efficient and Robust Reconstruction of Real-Valued Quantum States using **Hadamard Random Forests**
 
 ### Summary
 
-⚡ **Fast**: Reduces required quantum circuits from exponential to linear in the number of qubits  
+⚡ **Fast**: Reduces required quantum circuits from **exponential** to **linear** in the number of qubits  
 🎯 **Accurate**: Achieves 89% fidelity on 10-qubit real states using IBM quantum hardware  
 🧠 **Smart**: Uses a random forest over hypercube graphs for efficient sign reconstruction  
 
@@ -24,6 +20,9 @@ This is the code that accompanies the following paper: [arxiv.org/abs/2505.06455
 <img src="https://github.com/comp-physics/Quantum-HRF-Tomography/blob/master/assets/overview.png" height="300px"> 
 </div>
 
+Abstract:
+> Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an N-qubit system requires an exponentially increasing overhead with O(3N) distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many potential quantum computing applications, such as linear system solves, require only real-valued amplitudes. We introduce a readout method for real-valued quantum states that reduces the measurement settings required for state vector reconstruction to O(N); the post-processing cost remains exponential Ω(2N). This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields. We further implement the method to read out the solution from a quantum linear solver.
+
 ### Install 
 
 We recommend cloning the repo. and installing locally:
@@ -59,7 +58,7 @@ hrf.get_statevector(num_qubits, num_trees, samples, save_tree=True, show_tree=Tr
 ```bibtex
 @article{song2025reconstructing,
   author       = {Zhixin Song and Hang Ren and Melody Lee and Bryan Gard and Nicolas Renaud and Spencer H. Bryngelson},
-  title        = {Reconstructing Real-Valued Quantum States},
+  title        = {Hadamard {R}andom {F}orest: {R}econstructing real-valued quantum states with exponential reduction in measurement settings},
   year         = {2025},
   eprint       = {2505.06455},
   archivePrefix= {arXiv},