feat: use clearer abstractions + re-organise code + add partial trace + add pixi tasks

.gitignore

@@ -4,4 +4,9 @@
 *.egg-info
 
 # Binary files
-main
+build/
+build/*
+main
+*.mojopkg
+
+debug.mojo

Makefile

@@ -0,0 +1,4 @@
+# Makefile that forward every target to `pixi run`
+.PHONY: %
+%:
+	@pixi run $@ $(ARGS)

README.md

@@ -8,16 +8,14 @@ This project reimplements and extends the ideas from the following tutorial pape
 > *Michael J. McGuffin, Jean-Marc Robert, and Kazuki Ikeda*  
 > Published: 2025-06-09 on [arXiv:2506.08142v1](https://arxiv.org/abs/2506.08142v1) (last accessed: 2025-06-12)
 
----
 
 ## 🎯 Project Objectives
 
-* **Mojo Implementation:** Re-implement the approach from the paper in Mojo for more Pythonic readability and maintainability.
+* **Mojo Implementation:** Re-implement the approach from the paper in Mojo for more Pythonic synthax and better readability.
 * **Learning by Doing:** Gain hands-on experience with quantum circuit simulation to better understand the capabilities and limitations of classical simulation.
 * **Performance & Safety:** Leverage Mojo's strong static typing and compilation for blazing-fast and safe operations.
 * **Hardware Acceleration:** Utilize Mojo’s universal GPU programming support to accelerate simulations.
 
----
 
 ## ⚙️ Environment Setup
 
@@ -34,7 +32,16 @@ pixi install
 pixi run mojo build src/main.mojo && ./main
 ```
 
----
+
+## 🔥 Current Implementation(s)
+
+The current implemtnation uses State Vector which is an efficient method for simulating
+with high precision smaller scale qubits system of 20-30 qubits. It also allow for 
+easily accessible gradient computations.
+
+Another possible implemenation would be using Tensor Network, this method is effective 
+for large circuits, however with less precision in the calculations and with more
+expensive gradients computations.
 
 ## 📄 License
 

TODOs.md

@@ -0,0 +1,26 @@
+# TODOs
+
+A pure state is represented by a ket vector, e.g., $ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $, where $ \alpha $ and $ \beta $ are complex numbers satisfying the normalization condition $ |\alpha|^2 + |\beta|^2 = 1 $.
+
+## Ordered by Priority (5 ↑) / Difficulty (5 ↓)
+
+- 5 / 1 : density matrix calculcation from state vectors
+
+- 5 / 5 : Extend qubitWiseMultiply() to 2 and multiple qubits gates (Test it)
+
+- 4 / 3 : Implement measurement gates
+
+- 4 / 5 : Implement the computation of statistics: (6.5 and 6.6)
+
+- 3 / 2 :  Use a separate list for things that are not real gate to not slow down the main run logic
+
+- 3 / 3 : Implement naive implementation of the functions 
+    - matrix multiplication (but starting from right or smart)
+    - partial trace
+
+- 3 / 4 : Compile time circuit creation?
+
+- 3 / 2 : Reproduce table from page 10
+
+- 2 / 4 : qubitWiseMultiply() but for multiple qubits gates applied to non-adjacent qubits
+