How Qontinuum prices a circuit

Provider pricing is structurally heterogeneous — that's exactly why a comparison table is valuable. The catalog (src/qontinuum/cost/catalog.yaml) records each device under one of four pricing models; the estimator only implements the models, never device-specific code.

Models

per_shot (AWS Braket QPUs) cost = per_task + shots × per_shot. Braket charges $0.30 per task plus a per-shot rate that spans two orders of magnitude across vendors (Rigetti $0.000425 vs IonQ $0.08 per shot).

per_second (IBM Quantum Pay-As-You-Go) IBM bills QPU seconds ($1.60/s). Runtime is estimated with a parametric model:

seconds = overhead + shots × (per_shot_delay + depth × per_layer_time)

The default repetition delay (~250 µs) dominates: 4,000 shots ≈ 1 s of QPU time plus setup overhead. This is deliberately labeled an estimate — actual runtime depends on transpilation and device configuration.

gate_shot (Azure Quantum, IonQ devices) Azure bills IonQ by gate-shots: min_program + shots × (N1q·rate1q + N2q·rate2q). Multi-controlled gates are billed as 6×(N−2) two-qubit gates, which the circuit profiler applies. Error-mitigation defaults matter enormously: leaving it on raises the Aria minimum from $12.42 to $97.50 per program.

hqc (Quantinuum) Quantinuum bills in H-System Quantum Credits: HQC = 5 + shots × (N1q + 10·N2q + 5·Nm) / 5000, where Nm counts state prep and measurement. The PAYG dollar rate is not public, so Qontinuum reports the HQC quantity rather than inventing a dollar figure.

Honesty rules

• Every catalog entry carries the date its price was verified and source URLs.
• Estimates use the circuit as written; providers bill the compiled form, which can differ after transpilation to native gates.
• Devices that can't fit the circuit (qubit count) are shown as infeasible, not priced.
• Output is always labeled "estimates, not quotes."