Part 5 · 24-qubit algorithm
For 24 qubits we did not start with a large circuit and invent a story afterwards. We selected one local question: how much of a short domain-wall imbalance remains after 0.10 femtoseconds?
The active window
The model has four sites, six fermionic modes per site and twelve electrons. The central observable compares occupations on both sides of the middle and ranges from −1 to 1. Exact evolution gives an imbalance of 0.9872906000 at 0.10 fs.
A two-site window gives 0.9872156850. Their difference, 0.000074915, is below the predeclared threshold of 0.001, while the norm error also remains far below its threshold. This validates the four-site window for this observable and time—not automatically for spectra, longer times or the complete state.
Observable-specific first order
A first-order product formula does deviate globally from the exact state: at 12 qubits the state fidelity is 0.986226. Nevertheless, the error in the selected imbalance is only 0.000400 at 12 qubits and 0.000382 at 24 qubits. This illustrates why an observable-specific criterion can be sharper than demanding that the entire wavefunction be almost exact.
Routing 24 qubits
The frozen route transpiled for IBM Kingston to depth 632 with 693 CZ gates, passing the predeclared screens of depth at most 1000 and at most 2000 two-qubit gates. The experiment measures twelve central modes rather than reconstructing the full state.
Sources and reproducibility
Project status: 8 August 2026. Numerical values come from the frozen local research artifacts; the original claim boundaries are deliberately preserved.