Max-Cut

Source: examples/maxcut/README.md

Find a 2-colour partition of a weighted graph that maximises the total weight of edges crossing the partition.

QUBO formulation

• Input: num_nodes (int), edges (Vec of flat (i, j, w) triples, 3*|E| entries)
• Model: n binary variables, one per node. x[v] in {0, 1} selects the side of the cut.
• Objective: for each edge (i, j, w), add -w*(x_i + x_j) and +2w*x_i*x_j. Minimising this minimises -sum w*[x_i != x_j], i.e. maximises the cut.

DSL methods used

• problem.input() – declare typed calldata inputs
• problem.define_model() – allocate binary XQMX model
• problem.stow() – bind intermediate computations to named registers
• problem.range() – emit RANGE loops
• model.linear[i].add() – accumulate linear bias on variable i
• model.quadratic[i, j].add() – accumulate quadratic coupling between variables i and j
• problem.output() – declare typed output slots
• problem.sample.getline() – read a row from the sample bitstring

Pipeline overview

1. CP (xqcp) – build a random weighted complete graph, declare binary variables (one per node), and add linear/quadratic QUBO terms per edge.
2. Assemble – .xqasm text to bytecode via xquad.asm
3. Encode – run encoder on chosen XQVM to produce the XQMX model
4. Sample – solver runs SA/QPU/GPU over the model
5. Verify – verifier checks the sample is binary, then computes energy; this problem declares no constraints for it to check
6. Decode – decoder extracts the 2-colour partition

Usage

uv run python examples/maxcut/runner.py --seed 42
uv run python examples/maxcut/runner.py --n 6 --seed 7 -o /tmp/mc.json

Choosing a solver

Solver selection and install extras are the same for every example: see Using the Examples and Solving Overview. The default is dwave-cpu, and a non-default solver will not reproduce the canonical result.

Canonical output

example-smoke validates both interpreters produce valid == 1 with --seed 42 --solver dwave-cpu. The smoke test is invariant-based – it checks validity, not exact output.