ZKSF
Zero Kelvin Simulation Foundry
Certificate of Simulation Accuracy
Certificate ID
a5e78c20efb0477a
Certified: measured error bound 0.00e+00
Engine
pauli.cpu
Method
Pauli propagation (Heisenberg picture)
Shots
1000
Expectation
-1.137088528545
Discarded coeff. mass
0.000e+00
Error bound
0.000e+00
Converged
yes
How this certificate was produced
- This job used the certified ZCC-v0.1 path. The simulator was run with state renormalization disabled, so the final state's norm deficit equals the total weight discarded by every truncation performed during simulation. Call this quantity eps.
- Each individual truncation keeps the largest singular values and is therefore optimal by the Eckart-Young theorem, and eps is read directly from the final state rather than estimated or extrapolated. The quantity is measured in this one run, not inferred by comparing separate runs.
- The reported error bound is the square root of twice eps. It bounds the error on any single outcome probability when the individual truncation errors accumulate incoherently. That condition is not always met: a circuit performing N truncations admits an adversarial accumulation of up to the sum of sqrt(eps_i) over those truncations, and in deep circuits eps has been measured to understate the true infidelity by up to a factor of 9. The bound is therefore reported as an empirical result rather than as a consequence of that derivation.
- Across 334 runs at sizes where the exact answer is computable, including 290 constructed specifically to falsify it, the reported figure was never exceeded; the closest approach reached 49 percent of its value. Those checks require an exact reference and so extend to 20 qubits. Above that size the bound cannot be verified by direct comparison and no such evidence exists. Where a hard ceiling is required, use an exact or stabilizer engine.
- A second campaign of 1,543 runs to 24 qubits tested whether a stronger claim was defensible, using six circuit families of which three were built specifically to break the incoherence assumption. Of the 965 runs whose bound was below 1 and could therefore fail, the per-outcome claim above was never exceeded and came closest at 26 percent of its value. The same figure compared against total variation distance was exceeded in 23 of those runs and against state infidelity in 15. This certificate's statement is deliberately the per-outcome one: it is the strongest claim the evidence supports, and the two stronger readings are measurably false.
Circuit SHA-256: 0a765746853c2aea84b74042dc6c64d6e570d6d31b85dac7fd27949daf931292