What a job costs, before it runs
The first version of this experiment was sized by hand and cost roughly 3,750.62 credits of work. The cost formula now lives in the code: gate counts are read off the compiled circuit, the estimate is printed before anything is uploaded, and a batch outside the envelope is refused with the number named rather than quietly trimmed. No job submitted, no shots bought. Gate counts and HQC estimates only; the AUROC column is an ideal statevector score, not a measured result.
69 programs, 9 qubits, 1024 shots.
46 programs, 6 qubits, 256 shots.
Same question, same cohort, same verdict discipline.
The formula
HQC = 5 + (N1q + 10*N2q + 5*Nm) / 5000 * C
- N1q
- one-qubit gates
- N2q
- two-qubit gates, weighted 10x
- Nm
- measurements, inits and resets, weighted 5x
- C
- shots
The +5 is per circuit, so for small circuits the program count dominates the bill before a single shot is taken.
Reviewer feedback from a Quantinuum engineer
The envelope below is not ours. It came from a review on the hardware side, and each point is written here as a rule the run now follows, with the line that enforces it.
- Two-qubit gates: target 100 per circuit, hard stop 1000, absolute ceiling 2000 once noise is counted.
- Qubits: 4-20 for a demonstrator; 30+ is where classical simulation stops being easy.
- Shots: 128-512 is the normal range. 1024 only with a stated reason.
The sizing preflight reads the compiled circuit and refuses over-width or over-gate batches by name before upload.
- The +5 is charged per circuit, so for small circuits the program count dominates before a single shot is taken.
- A two-qubit gate counts ten times a one-qubit gate.
- Cost is linear in shots — doubling shots doubles the bill.
Gate counts come off the compiled circuit, not a hand-typed estimate, and the per-program cost table prints at submit time.
- A million shots is not possible on Helios (98 qubits).
- Allowable shots fall as the two-qubit gate count rises.
- The two-qubit fidelity spec and the shot count belong in the same sentence.
Every quantum leg is labelled H2-Emulator, and the shot count is published next to the gate census rather than on its own.
- 10,000 credits is a normal project; 100,000 is a showcase.
- Cheaper is better — a smaller job that answers the question beats a large one that impresses.
A per-run budget is reserved up front; an over-budget batch is refused with the number named, never quietly trimmed.
The operating envelope
| Knob | Limit | Why |
|---|---|---|
| Two-qubit gates per circuit | target <= 100, hard stop 1000, absolute ceiling 2000 with noise | Fidelity collapses past this on ion traps. |
| Qubits | 4-20 for a demonstrator; 30+ before classical simulation stops being easy | Below 20 a laptop reproduces the result. |
| Shots | 128-512 typical; 1024 only with a stated reason | Cost is linear in shots. |
| Circuits per experiment | Keep low — each carries +5 HQC | 69 circuits is 345 HQC before a single shot. |
| Budget | 10,000 HQC normal project, 100,000 HQC showcase | Cheaper is better; the guard refuses rather than overspends. |
A million shots is not possible on Helios (98 qubits). Allowable shots fall as the two-qubit gate count rises, so the two-qubit fidelity spec and the shot count belong in the same sentence.
Candidate circuits, costed side by side
Three feature maps for the same classification question. Gate counts come from the circuit itself; the score column is an ideal noiseless calculation used only to choose between designs, never reported as a measured result. Classical floor: Logistic regression with balanced class weights — AUROC 0.5.
| Design | Qubits | Depth | 1-qubit | 2-qubit | Credits / program | Batch | Ideal score |
|---|---|---|---|---|---|---|---|
| Angle encoding + entangling ring | 6 | 15 | 24 | 10 | 12.88 | 592.7 | 0.75 |
| Second-order ZZ feature map | 6 | 35 | 34 | 20 | 18.52 | 851.77 | 0.75 |
| Hardware-efficient ansatz, 2 layerschosen | 6 | 23 | 48 | 20 | 19.23 | 884.75 | 1 |
Generated Sun, 13 Sep 2026 01:48:42 GMT by Offline sizing analysis (pytket gate census + ideal statevector). Nothing on this page was submitted or billed.