How I built a quantum-inspired route optimizer in pure Python (no quantum hardware)

#opensource #python #productivity #machinelearning

The problem

Ever wondered how delivery companies figure out the best route for their drivers?
It's called the Travelling Salesman Problem (TSP) — and it's brutally hard to solve
optimally as the number of stops grows.

I wanted to explore quantum-inspired approaches to this problem — algorithms that
borrow ideas from quantum physics but run on regular CPUs. No quantum computer needed.

What is QUBO?

QUBO stands for Quadratic Unconstrained Binary Optimization. It's a mathematical
framework where you express any optimization problem as:

Binary variables (0 or 1)
A matrix of coefficients
Minimize the total "energy"

Quantum annealers (like D-Wave) solve QUBO natively. But quantum-inspired algorithms
simulate this classically — and that's exactly what I built.

What I built

quasar-solver — a pure Python QUBO optimizer with:

QUBO class: sparse dict representation, energy computation
SimulatedAnnealingSolver: multiple restarts, tunable beta schedule
TSP converter: encodes city routing as a QUBO matrix
Interactive web demo — click to place cities, watch the solver find the route

🔴 Live Demo — no install needed, runs in browser

Quick usage

from quasar_solver import QUBO, SimulatedAnnealingSolver

q = QUBO()
q.add(0, 0, -1.0)  # linear term
q.add(1, 1, 2.0)   # linear term  
q.add(0, 1, -3.0)  # quadratic term

result = SimulatedAnnealingSolver(seed=42).solve(q)
print(result.best_sample)   # [1, 1]
print(result.best_energy)   # -2.0

How TSP becomes QUBO

The key insight: use one-hot encoding. Variable x[i][t] = 1 means city i
is visited at timestep t.

Two constraint types become penalty terms:

Each city visited exactly once
Exactly one city per timestep

The solver minimizes total distance + penalties simultaneously.

Results

On a 6-city random instance, the solver finds a valid tour in under 10ms on CPU.
The web demo uses 2-opt moves in JavaScript for instant visual feedback.