Every value comes with the bound on its own error.

Send a circuit and the observables you care about. Each expectation value is returned with a certificate: the sum of every term dropped on the way. The exact answer lies within that distance of the reported one, unconditionally, for any circuit and any product initial state. When the certificate is 0 the answer is exact.

Width is free. The bundle is the cost.

A local observable on a depth-4 random circuit costs the same 16–30 thousand terms whether the register has 12 qubits or 1,000, because the cost is the light cone. Your tier sets the largest bundle a job may carry; the response tells you how large it got.

Exact regime

Depth ≤ 5 on a 1D brickwork, any width: the bundle fits, the certificate is 0, the value equals a dense oracle to 1e‑15 wherever an oracle exists.

Certified regime

Deeper, or long-time interacting dynamics: terms below τ are dropped into the certificate. The TFIM quench at 100 sites reports 2.3e‑6 and lands within 4.1e‑7 of an MPS oracle.

Refused, with numbers

If the bundle would exceed your budget the job stops, tells you the size it reached and at which gate, and charges nothing. No silent truncation, no partial answer dressed as a full one.

The record behind this page.

Workload	Claim	Oracle	Observed	Timing
TFIM quench, 100 sitesCondensed matter	Mean magnetisation and bond correlator after 20 Trotter steps (J=h=1, T=1), certified.	MPS oracle, agreement 4.1e-7 (the oracle's own floor)	1.21M-word bundle, certificate 2.3e-6; bundle grows linearly in width (≈12k words per site)	508 s single-core Python, an upper bound for the production port
Same run, 16 sites: state side vs observable sideCondensed matter	A cluster-materialising state register caps at rank 14 on this machine and stalls silently.	dense state vector	state side 5.9e-2 off while reporting converged; observable side 3.0e-10 off	14 s
TFIM hard quench, 200 sites, fermionic chartCondensed matter	Order parameter after a T=4 quench (16 steps of dt=0.25) — the case where the Pauli bundle blows up — exact via a Pfaffian readout.	dense state vector at n ≤ 14: max deviation 3e-14	exact, no certificate needed; the same quench at 12 sites cost 6.9M words on the Pauli side	7.7 s at 200 sites, 0.57 s at 100
Depth-4 brickwork, width 12 to 1,000Random circuits	Mid-chain ⟨Z⟩ on √iSWAP brickwork with random single-qubit layers; the cost is the light cone, not the width.	dense at n=12: 3.3e-16	16k–30k words and 8 support qubits at every width	0.06–0.5 s
The wall, statedRandom circuits	Exact through depth 5 at 50 qubits (684k words). At depth 6 the bundle passes 6M words and the certificate stops certifying. At depth 14 on 8 qubits the observable fills all 65,535 words.	dense at n=8, depth 14: 5.2e-16 (exact, because all words were kept)	this is the #P wall on the readout side; it is reported, not hidden	1.6 s at depth 5
Zero-coordination foldDistribution	One observable split into 64 shards, each transported independently, merged by addition.	the serial run	⟨Z⟩ within 8.6e-10 of serial (truncation-order effects only)	16 sites, 20 Trotter steps

Observable-side record cq-front-2026-09-01, measured 2026-09-01 against numpy dense statevector (n ≤ 20), qiskit-aer 0.17.2 matrix-product state (n ≥ 24), Majorana-chart Pfaffian (matchgate circuits). Raw record. Width-side record cq-prod-2026-08-22-ed64918e, revision 5a0d43a69f5e. Both on the evidence page.

When the bundle blows up, suspect the representation first.

On 2026-09-01 the order parameter of a hard TFIM quench cost 6.9 million terms at 12 sites and the certificate stopped certifying. The bond correlator in the same run needed 276. The difference is not the physics: under a Jordan–Wigner map the bond term is a fermion bilinear and the single-site term is a string. In the fermionic chart the same quench is a Pfaffian, exact at 200 sites in 7.7 seconds.

That chart is live on the route. A circuit is tested gate by gate: if every gate is a nearest-neighbour matchgate (Z-axis single-qubit rotations with XX, YY or iSWAP-type couplings, or the same circuit written with X rotations and ZZ couplings) from a Fock or uniform |+⟩ product state, the job runs in the Majorana chart — exact, one credit per observable, any width up to the 256-qubit call limit — and the response says chart: "fermionic". Anything else takes the Pauli bundle with its certificate. Interacting models (XXZ, Hubbard) have no such chart; there the certificate is the honest answer, and past 24 sites it says so.

Others bound their truncation too. IBM's operator-backpropagation add-on and at least one hosted Pauli-path service return the same class of bound (a norm of the dropped coefficients). The difference here is what surrounds it: the route recognises and reports the exact regime, switches to the fermionic chart when the circuit allows one, takes 256 qubits per call priced by bundle rather than by minute, and returns a citable record. The tightness of the bound against a dense oracle is a measurement, and it is next on the evidence page.

Every finished job is also a citable record: a public page with the values, the certificate, the circuit and a BibTeX entry, in a hash-chained ledger a reader can verify. Share the link; the reader needs no account.

What it does, and what it does not.

Stating the boundary next to the result is the point. In a field where every benchmark is self-reported, the vendor that publishes its own limits is the one worth checking.

In class

Exact expectation values and typed observables on structured circuits, at widths no state vector holds.
Local observables on deep circuits: exact through the light cone (depth 5 in a 1D brickwork), certified beyond it — the cost is set by depth, not width (measured n=12 to 1,000).
Condensed-matter quenches: certified observable transport (TFIM to 100 sites within 4e-7 of an MPS oracle) and exact matchgate dynamics in the fermionic chart (TFIM order parameter at 200 sites in 7.7 s).
QEC: code-capacity thresholds at any distance in O(n) per shot, and the exact coherent-error logical channel of the rotated surface code at d=3 and d=5.
Analytic ground truth a third party can check without trusting us.

Out of class

Full-distribution shot sampling. No counts are produced; `materialized_gate_count` is 0 by construction.
Scrambled circuits at depth of order the width: the observable fills the 4^n Pauli space (65,535 words at n=8, depth 14). That is the #P wall on the readout side, and no representation moves it.
Interacting spin models at long times (XXZ, Hubbard): the value is returned with its certificate, and past 24 sites the certificate stops certifying.
Any claim about hardware fidelity. This is a classical engine, not a QPU.