Y basis · tools
QUBO / QAOA Workbench
Pick a combinatorial problem, fill in an instance, and watch it turn into a QUBO you can check — then into an Ising Hamiltonian, a QAOA landscape, and finally a block of PennyLane you can paste into a fresh notebook and run.
Everything happens in this tab. Nothing is uploaded, nothing is fetched, and there is no account — the only thing that leaves the page is code you copy.
Where the limits are
A statevector doubles with every qubit, so simulation, brute-force checking and the landscape view stop at 20 qubits. Code generation never stops — above the line you still get the full formulation and a program to run elsewhere. Penalty weights come from published closed-form bounds, so a formulation the tool cannot brute-force is still correct by construction.
Save this instance, or resume one
A save code carries the whole formulation, so pasting one back reopens every step it is big enough for — you can come back to the middle of the pipeline, not just the start. It is a string of text and nothing else: no account, no upload, nothing stored anywhere but wherever you paste it.
Every problem here ends up as the same object: a square matrix Q
over binary variables, plus a constant offset. Minimising
over all assignments of the bits is the problem. Constraints do not appear separately — they are folded in as penalty terms weighted by λ, chosen large enough that breaking a constraint can never pay for itself. Every λ below is the published closed-form bound for that problem, so the formulation is sound even at sizes nothing here can check.
The Q matrix
Which qubit is which
Does the formulation actually work?
The same energy, rewritten over spins s = 2y − 1. Nothing is
being solved here and nothing is lost — it is a change of variables, and the point of the
step is that you can see it is one. These three things are what a simulator or a device
actually takes: the local fields h, the couplings
J, and the constant offset.
QAOA, simulated here in the tab. The circuit is built from the Hamiltonian in Step 2, run on a hand-written statevector, and measured against the true optimum that Step 1 brute-forced — which is why none of this exists above the cap: there is nothing to measure against, and nothing small enough to simulate.
Too large to analyse here
Above ~20 qubits, this tool generates code but can’t run, verify, or analyze the landscape in your browser. You’ll get the formulation and PennyLane code to run yourself.
A self-contained cell: it installs what it needs, defines this instance inline, seeds its own randomness and prints a result. Paste it into a fresh notebook and it runs, with nothing to fill in. This step is never capped — above the limit it is the whole offering, and it is marked as unverified rather than withheld.