Quantum Modeler · 0/1 Knapsack

Choose what matters. Stay within capacity.

Select items to maximize value without exceeding a weight limit. Translate that decision into a quantum model, explain the mathematics, run a small QAOA circuit, and check the result against an exact classical solution.

The eight-qubit execution limit includes item decisions and capacity slack. Larger targets are projections only. QAOA samples can violate the capacity constraint; those samples are never reported as valid solutions.

Items, value, and capacity

Executable instance Items (weight value, one per line) Rows are Item 0, Item 1, etc. Positive integers only: weight 1–127, value 1–1000. At most seven items, with room for slack qubits. Capacity

Execution settings QAOA depth Measurement shots Sampling seed

A bounded grid chooses angles by minimizing expected penalized energy. Opening the explanation uses the completed result and consumes no additional run.

Target scale · projection only Target item count (optional) Target capacity (optional) Supply both or leave both blank to project the current size. Estimates assume positive integer item weights and the same binary-slack encoding. No larger item list or solution is invented.

Ready to validate a small selection problem.

Results and explanation describe the last completed build. Rebuild after changing inputs.

Explain this model

From business interpretation to objective, Hamiltonian, circuit, complexity, and limitations.

EXECUTED

Small-instance QAOA

Open in Simulator

VERIFIED

Selection and exact reference

EXECUTED · Feasibility matters

Capacity-feasible means selected item weight ≤ capacity. The penalty equality also requires sampled slack to match the unused capacity. Conditional expected feasible value averages only over feasible probability mass.

A lower penalized energy does not guarantee a better measured selection. Infeasible selections remain visible in the distribution.

PROJECTED — NOT EXECUTED

Target encoding resources

EXECUTED · Measured candidates

Top 16 sampled bitstrings. Item bits come first; slack bits follow in order 1, 2, 4, … . Value and weight are classically decoded from item bits.

Bits	Count	Probability	Value	Weight	Capacity	Slack equality

Full probability distribution

Bits	Count	Probability	Value	Weight	Capacity	Slack equality

Circuit artifacts

Generated DSL

OpenQASM 2.0

NOT CLAIMED

Encoding evidence, explicit limits

This is an ideal, noiseless simulation on classical hardware. It demonstrates a small formulation and independent verification, not quantum advantage, QPU execution, physical-qubit requirements, fault tolerance, or large-scale performance. No production resource-allocation quality is guaranteed.