Hybrid execution

The boundary

A hybrid loop has two programs. The classical program owns the search state: angles, penalties, candidate bitstrings, and stopping rules. The quantum program owns a circuit evaluated at those angles. The only values that need to cross the boundary are the parameters going in and the estimates coming out. Amplitudes usually stay inside the quantum step.

That boundary is where reproducibility is won or lost. Log the parameter vector, the circuit identity, the shot count, the seed, and the returned estimate. A plot of “energy versus iteration” without those fields cannot be audited.

Variational loops

QAOA and related variational methods alternate a cost-encoding unitary and a mixer unitary, repeated for a chosen depth, with free angles. A classical optimizer — a derivative-free method is common when gradients are noisy — proposes the next angle vector. Each proposal costs a batch of shots or an exact expectation if a state vector is available.

The optimizer sees noise as part of the objective. If shot noise is larger than the improvement the optimizer expects, the loop randomizes. Fix shots, or increase them when the step size shrinks. Depth adds expressiveness and also adds noise on hardware; a shallow circuit plus a classical repair is often the more stable research design.

θ_{t+1} = Optimizer( θ_t ,  Ê[C] from circuit(θ_t) )

Quantum proposal, classical certificate

Kryptur’s combinatorial work treats the quantum step as a proposal distribution. Samples or low-cost strings suggest candidates. A classical refinement improves them under the real constraints. A formal check, where the paper uses one, accepts or rejects the refined object. The object that is certified is the one that passed the classical check, not the raw quantum string.

This division matches the way the research is meant to be read. Quantum hardware or simulation explores a biased set of bitstrings. Classical code enforces the specification. Publishing only the quantum sample omits the step that made the answer admissible.

• Proposal: circuit samples or a state-vector ranking.
• Repair: greedy or exact classical improvement under the original constraints.
• Check: a proof, a solver status, or an exhaustive comparison on a published instance.

Where to go next on this site

The circuit model, the state vector, tensor contraction, sampling, and noise notes are the vocabulary for reading a Kryptur hybrid paper. They are concept notes written here. They are not a vendor software manual, an install guide, or an API catalogue. For the portfolio that uses this vocabulary on published problems, follow the research links at the foot of the page.