Every other tool answers "run my method." Atlas also answers the money question: what would this circuit cost on a real QPU, and what does the classical route cost instead? The number is built from a formula you can see, with assumptions you can edit — labeled published / measured / derived, never a black box.
deploy/app/economics.py$0.30 task + 10,060 shots × $0.08/shot, published Braket pricing. At research-grade precision (ε=3e-3, ~112k shots) the same job is ≈ $8,900. Open the panel and recompute — that is the point.To pin an expectation value to additive error ε you need shots that beat shot-noise (error ~ 1/√N):
N_base = ⌈ 1 / ε² ⌉ε=1e-1 → 100 · ε=1e-2 → 10,000 · ε=3e-3 → ~111,111. derived (textbook shot-noise). Vendor floors apply (e.g. IonQ error-mitigation minimum 2,500 shots).
Real hardware is noisy, so a usable expectation value needs error mitigation, whose sample overhead grows exponentially with circuit volume × noise (probabilistic error cancellation):
N = N_base · γ², γ² = e^(4·λ), λ = ε_g · n₂qpublished bound — Quek/Eisert arXiv:2210.11505, Takagi arXiv:2109.04457. n₂q = two-qubit gate count, ε_g = per-gate error (next section).
ε_g or the mitigation model move the QPU cost by orders of magnitude. That is exactly why Atlas exposes ε_g and the formula as editable and sourced — the honest answer to "why this model?" is "PEC, published, and you can swap it," not "trust us." We label it published, never measured.The exponent rides on ε_g, so Atlas uses per-device values, not one generic number:
| Device | ε_g (2-qubit) | Provenance |
|---|---|---|
| IBM (Heron r2) | 2.0e-3 | measured — Atlas's own ibm_kingston RB (2.02e-3 isolated; 3.42e-3 EPLG layered) |
| Rigetti | 5.0e-3 | published — 99.5% 2q fidelity |
| IQM (Garnet/Emerald) | 5.0e-3 | published — 99.51% |
| IonQ (Forte/Aria) | 3e-4 | vendor-claimed — no hard public 2q figure; optimistic, flagged uncertain |
The IBM number is measured on our own hardware runs — that calibration data is part of the moat, like the corpus. The rest are published/claimed and editable.
Most naïve estimators invent a $/shot for IBM. IBM doesn't bill per shot — it bills per minute of QPU time. Atlas branches:
per-shot (AWS Braket): cost = task_fee + N · per_shot per-minute (IBM): cost = runtime_min · rate_per_minpublished tariffs — AWS Braket (IonQ $0.08/shot + $0.30/task; Rigetti $0.000425; IQM/AQT/QuEra) · IBM plans (Open free · Pay-As-You-Go $96/min · Flex $72/min · Premium $48/min). Verify: AWS Braket pricing · IBM Quantum plans.
The whole verdict is a comparison, so the classical cost is measured, not guessed: Atlas times the real MPS/tensor contraction (quimb) for the circuit and prices the wall-clock at a cloud-CPU rate. The reference machine is a dev Apple M4 (24 GB) — see the per-estimator ceilings on the Evidence page.
A laptop that settles the circuit in milliseconds at near-zero cost, versus the QPU job above, is the "don't spend" verdict in dollars.
IonQ Forte, a small tractable circuit a laptop runs in ms:
| Precision ε | Shots (incl. mitigation) | QPU $/job |
|---|---|---|
| 1e-1 / 3e-2 | 2,500 (vendor floor) | $200.30 |
| 1e-2 (casual) | ~10,060 | ≈ $805 |
| 3e-3 (research-grade) | ~111,781 | ≈ $8,900 |
Every row is recomputable from §1–4 with the published pricing; the panel lets you change vendor, ε and campaign size and watch the number move.
ε_g from our own QPU runs); (3) per-shot-vs-per-minute modeled correctly; (4) full auditability — every term labeled and sourced. The page you are reading is the moat: a cost number you can recompute, versus a black-box calculator you can't.