Optimization Lab

QUBO Solver

Build a small binary quadratic objective, inspect the Q matrix, and compare exact search against a greedy local-search baseline.

Template

Three binary variables choose a graph partition. Lower energy means more cut edges.

0.0
Best000
Energy0.00
Greedy000 / 0.00

Best bitstring 000, energy 0.00, feasible.

Learning mode

Mission briefingIntermediate / 9 min

Turn decisions into energy

A QUBO is a scoreboard for yes/no choices: every bitstring gets an energy score.

Edit one matrix cell and watch which bitstring becomes the best solution.

Definitions on demand

QUBO

A quadratic objective over binary variables with no explicit constraints.

Penalty

An added energy term intended to make rule violations unattractive.

Feasible

An assignment satisfying the selected real-world rule, independent of its raw objective energy.

Q Matrix

Only the diagonal and upper triangle contribute to E(x) = x^T Q x.

3 variables
A
B
C
A
B
C

Energy Ranking

#1

000

feasible

0.00
#2

001

feasible

0.00
#3

010

feasible

0.00
#4

100

feasible

0.00
#5

011

feasible

2.00
#6

101

feasible

2.00
#7

110

feasible

2.00
#8

111

feasible

6.00

Best-solution energy decomposition

All active terms contribute zero.

Total0.00