Quantum Optimization - Introduction to QUBO

What exactly is a QUBO problem, and why does it appear everywhere in quantum optimization? In this video, I explain QUBO step by step using the MaxCut problem as a running example. We start from a weighted graph, understand what MaxCut means, place QUBO in the broader optimization landscape, and then derive the QUBO matrix mathematically. After that, we switch to a Jupyter notebook and solve the problem by brute force to see why QUBO becomes hard as the problem size grows. This video covers: - MaxCut intuition using a small weighted graph - Continuous vs discrete optimization - Convex vs non-convex optimization - Combinatorial optimization and NP-hardness - Why QUBO matters in quantum optimization - Matrix form of a QUBO problem: x^T Q x - Linear and quadratic coefficients in Q - How MaxCut is formulated as QUBO - Brute-force solution in Python - Runtime scaling with problem size GITHUB REPO: https://github.com/supreethmv/Quantum-Algorithms-and-Applications If you want to understand how optimization problems are translated into forms that quantum hardware can work with, this video is a practical starting point. Chapters: 00:00 Intro 00:16 MaxCut intuition 00:56 Why MaxCut becomes hard 01:32 Continuous vs discrete optimization 03:20 Combinatorial optimization 04:40 Where QUBO fits 05:32 What a QUBO solver takes as input and returns as output 06:03 Understanding the matrix form x^T Q x 07:15 Decoding the binary solution vector 07:42 Building the Q matrix from the graph 10:44 Linear vs quadratic coefficients 13:47 MaxCut objective as a QUBO expression 15:27 Jupyter notebook walkthrough 18:24 Brute-force solving 20:00 Exponential runtime scaling 20:36 Outro #QUBO #QuantumComputing #Optimization