Executable classical Boltzmann-style sampling illustration; not QAOA or quantum measurement.
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Penalty and Sampling Sweeps: What Our Research Page Does and Does Not Show
A changing percentage can look scientific even when the computation behind it is misunderstood. The Penalty & Shot Sweeps page is therefore best read with its backend in view: its current runner uses a classical Boltzmann-style energy-weighted sampler. It does not execute QAOA, evolve quantum amplitudes or measure a quantum circuit.
That distinction matters because the separate Resilience Lab does run a QAOA circuit on a local classical statevector simulator. Sharing a toy network does not make every page using that network a quantum experiment. The research sweep is an illustration of energy weighting and finite sampling; the circuit lab is a different executable workflow.
What the penalty experiment varies
The toy decision is to select two of six optional network links. The sweep's energy calculation rewards restored coverage and adds a penalty when the selection count differs from two. Its penalty experiment changes the coefficient across a fixed list while keeping its sample budget and seed fixed.
The runner constructs probabilities from an exponential weighting of energy, normalizes them and samples from that distribution. This is a classical distribution chosen by the implementation. A higher feasible fraction in that sampler is not evidence that a QAOA optimizer learned a better state, because no QAOA optimizer ran on this page.
The sweep also should not be treated as a byte-identical implementation of the circuit lab's Hamiltonian for every invalid bitstring. The research runner computes its own coverage/penalty model. A defensible cross-backend comparison must check the full objective encoding rather than infer equivalence from matching feasible examples.
What the sample-budget experiment varies
The second experiment keeps a penalty value and seed fixed while changing the number of draws. More samples can change the best observed feasible selection and make an empirical fraction less volatile. They do not change the underlying distribution used by this runner.
The interface retains a Shot Budget research label, but its explanatory text identifies these as classical samples, not quantum shots. Read that qualification with the table. A best observed score is an extreme among the draws made; it is not an expectation value or a guarantee about a later independent run.
Why feasibility and quality are different
A sample can satisfy the exactly-two constraint and still choose links with a weaker objective value than another feasible selection. Conversely, a large penalty can favor validity without proving that a useful objective distribution has been learned. Report the valid-sample fraction and objective quality separately.
The optimum-hit column compares an observed feasible result with the reference coverage for this fixed toy. It does not time a classical solver against quantum hardware, establish a general approximation guarantee or demonstrate an operationally resilient network. The toy omits the many capacities, costs and failure combinations that a real deployment would require.
Where actual QAOA evidence belongs
For the circuit lab, useful evidence includes the executed operations/backend, depth, optimized angles, measured counts, constraint checks and a separately computed classical reference. The original QAOA paper by Farhi, Goldstone and Gutmann describes a quantum approximate optimization framework; it does not make an arbitrary energy-weighted random sampler an instance of that algorithm.
A simulator is also not quantum hardware. It can execute a mathematically specified circuit on an ordinary computer, which is valuable for inspection, but it does not establish a hardware speed advantage. Our beginner lab guide explains that separate workflow.
When to use this illustration
Use the sweep to learn how one explicitly stated classical model responds to penalty weight and finite draw count. Keep its tables with the model description, seed and sample budget. Avoid exporting an attractive fraction without the disclosure that explains how it was generated.
For a reproducible reading exercise and an experiment log template, follow the sweep guide. For proposed circuit extensions alongside current classical illustrations, read the research roadmap: five new notes are proposals, not completed benchmark results.