Learning Notes
Plain explanations of qubits, vectors, matrices, measurement, entanglement, and algorithms.
Quantum • AI • Optimization
Research notes and experiments for building intelligent systems from first principles.
Enraiq is a public lab for learning quantum computing, using AI as a research assistant, and testing ideas on real business optimization problems.
Research tracks
Built for reading, testing, and improving over time.
Qiskit Experiments
Reproducible circuits such as Bell states, teleportation, Grover, QFT, VQE, and QAOA.
AI-Assisted Research
Using AI to understand papers, verify code, generate hypotheses, and simplify complex math.
Business Optimization
Models for lead routing, priority scoring, allocation, scheduling, and decision intelligence.
Active experiment path
Turning a real business routing problem into testable models.
The long-term research thread starts with legal lead routing: assign each incoming lead to the best-fit customer while balancing filters, priority, schedule, order volume, and likely conversion quality.
Rule-based baseline
Start with clear matching rules for location, practice area, customer filters, availability, and order balance.
Classical optimization
Convert the routing decision into scores, constraints, penalties, and measurable tradeoffs.
Quantum-inspired model
Explore QUBO-style formulations and small QAOA prototypes in Qiskit on synthetic datasets.
Compare and document
Measure what improved, what failed, what scaled poorly, and what needs deeper study.
Roadmap
From beginner foundations to applied research projects.
The goal is not to repeat generic quantum explainers. The goal is to document a serious learning path and convert concepts into working experiments.
Phase 1Linear algebra, probability, complex numbers, Qiskit basics.
Phase 2Known quantum circuits and algorithm reproductions.
Phase 3Classical optimization baselines and AI scoring models.
Phase 4Quantum-inspired and hybrid experiments for decision systems.
Latest writing
Notes and experiments
How a Parameter Changes Rank: Pivot Variables, Free Variables, and Special Solutions
A step-by-step study of Strang's parameter-dependent rank example, showing how pivots identify pivot variables, why nonpivot variables are free, and why c=4 causes the rank to drop and the nullspace to gain an extra direction.
Read note →Understanding Rank and Rank-One Matrices: Pivots, Redundancy, and Nullspace Geometry
An intuitive study of matrix rank, why pivots measure independent information, how special nullspace solutions expose redundant columns, and why rank-one matrices have the form A=uv^T.
Read note →From Entangled Clocks to Local Realism and Hidden Variables
Why perfect entanglement correlations naturally suggest predetermined answers, what locality and realism mean, and why Einstein was led to the idea of hidden variables.
Read note →