experimental · research and evaluation use

Certified answers where there is no state vector.

Deep circuits, condensed-matter quenches, error-correction experiments: the regimes every simulator fails in are the regimes a researcher most needs a number for. Catalyst‑Q moves the observable instead of the state, and returns every value with an error certificate — 0 when the answer is exact, an unconditional bound when it is not. The cost is the size of the observable, not the number of qubits.

Exact through the light cone. Certified beyond it. The wall is stated on every page, with the measurement that found it — the scope is published.

Random circuit, depth 4, mid-chain ⟨Z⟩
1,000 qubits · 0.5 s · exact
TFIM quench, order parameter, 200 sites
7.7 s · exact
Surface code d=9, code-capacity threshold
4 ms per shot · 81 qubits
Width-side record, exact observable
1,000,000 qubits · 3.2 s

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.

the mechanism

The state is never built. The observable is what moves.

01

Heisenberg picture

A Pauli observable is pulled backwards through the circuit. Clifford gates permute it with a sign; other gates split it into a small weighted bundle. Nothing of size 2n ever exists.

02

The certificate

Terms below a salience threshold are dropped, and every dropped weight is added to a bound: the reported value is within that bound of the exact one, unconditionally. A certificate of 0 is an exact answer.

03

The right chart

When a bundle grows, it is usually the representation and not the physics. The TFIM order parameter that cost 6.9M terms in the Pauli chart is a 200-line Pfaffian in the fermionic one — exact at 200 sites in 7.7 s.

04

The wall, measured

Scrambled circuits at depth of order the width fill the Pauli space: 65,535 of 65,536 terms at 8 qubits, depth 14. That is the #P wall on the readout side. It is reported as such, never rounded off.

How the certificate works Download the raw record

scope

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.

who this is for

Four buyers, one meter.

Condensed-matter and many-body groups

Quench dynamics past the state-vector ceiling, with a number you can put in a paper and a certificate a referee can check.

QEC teams

Coherent-error logical channels that stabiliser tools cannot express; threshold sweeps at any distance in milliseconds per shot.

Algorithm teams with metered hardware

The observable you were about to pay a QPU to estimate, computed first. One prevented $6,000 run pays for a year.

Toolchain vendors and assurance

A correctness oracle in CI above the width your own simulator reaches, and an independent verification record for a claim you are evaluating.

Compute one observable.

Create an account, open the console, and run your own circuit. The free tier needs no card and carries a 60,000-word bundle budget — enough for a depth-4 random circuit at any width.

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