Quantum Modeler · Capacitated Vehicle Routing

Capacitated Vehicle Routing

Cover every customer exactly once using at most the supplied number of identical vehicles. Minimize total distance over the complete set of capacity-feasible depot tours.

Execute at most 8 total qubits using an ideal classical statevector simulator. Symbolic scaling does not execute or solve a larger instance.

Build your problem

Presets replace problem inputs. Your execution and projection settings stay as entered. Edit any input, then build to calculate new results.

Depot 0 has no demand. Each complete candidate tour consumes one decision qubit; fleet slack also counts toward 8. Routes return to depot 0. This model has no time windows, heterogeneous vehicles, or split deliveries.

Problem inputsSymmetric distances — one matrix row per lineSpace or comma-separated nonnegative distances. The diagonal must be zero and both directions must match exactly. Node 0 is the depot or fixed start.Customer demands — customers 1, 2, …Capacity per vehicleMaximum vehiclesAll demands and capacities are positive integers. A demand above capacity is accepted as an infeasible instance. Candidate tours are complete, with reverse duplicates removed.

Large-target projection (optional)

Leave all target fields blank for this exact encoded input. Enter independent target statistics to estimate resources; only the small instance is executed.

Grey examples are suggestions; enter values for your own target.Target customers (excluding depot)Maximum target vehiclesOptional target vehicle capacityOptional demand lower bound (every target customer)Supply customers and vehicles together. Capacity and minimum demand are an optional pair that bounds route length; omit both for the unrestricted upper bound. No customer demands or distances are copied from the small instance. Counts do not establish target feasibility or compiler eligibility.

Use the Quantum Compiler for native compile-only inputs within its resource limits. A projection does not construct or compile the target.

Execution settingsMeasurement shotsSampling seed

Depth 1 QAOA, at most 64 parameter evaluations. One completed build uses one run when usage limits are enabled.

Qubit budget

All decision and auxiliary variables count toward the limit. The API validates all constraints before reserving a run.

Read the mathematical methodology

Ready to validate a small instance.

Results describe the last completed build.

Explain this model

EXECUTED

Small-instance simulation

VERIFIED

Independent classical reference

ENCODING RESOURCES

Encoded input resources

Sampled states

Bits	Count	Probability	Penalized energy	Feasible objective	Penalty constraints	Assignment

Full probability distribution

Bits	Count	Probability	Penalized energy	Feasible objective	Penalty constraints	Assignment

Circuit artifacts

x0 is the leftmost assignment bit. Measurements map xi → q[i] → c[i]; tools displaying c[N−1]…c[0] require register-order conversion.

Open in Simulator

Variable mapping

QUBO and Ising coefficients

Generated DSL

OpenQASM 2.0

Routing and scheduling models

TSP · Job Scheduling · Vehicle Routing. Tiny validated examples execute within eight total qubits; larger inputs use the Problem Compiler.

No quantum advantage, real-QPU performance, physical-qubit requirement, or production-scale solution quality is claimed.