A forced gold-colour model on 56 qubits of IBM hardware

Part 9 · model-assisted colour and hardware

We did not merely attach a fast, empirically calibrated gold colour to the 56-qubit model. We inserted it into the Hamiltonian as an energy correction and ran exactly one validated experiment on IBM Marrakesh. The forced model signal remained clearly visible in the expected direction.

The short result: the strongest ideal cell response was 0.376331. Raw hardware returned 0.255105 and the linear zero-noise estimate returned 0.315258. Their direction cosines with the ideal response pattern were 0.966469 and 0.974583.

What does “forced” mean?

The earlier optical calibration produced a visually gold-like colour, #F9E29D, with CIELAB Delta-E-76 equal to 4.34 relative to measured single-crystal gold. This passes our broad “visually gold-like” threshold below 6, but not the strict threshold below 3.

The colour fit contained an energy shift of 0.728883 eV. For this experiment we applied that value as an empirical scissors correction to the twelve unoccupied eigenmodes of the 56-mode Hamiltonian. The 44 occupied modes, their projector, and particle number were preserved. The one-particle gap increased from 0.647228 to 1.376111 eV.

This is deliberately a model-assisted intervention. The shift is not a G0W0 result and was not derived without measured gold data. The experiment asks a narrower question: does a model change calibrated to gold colour remain recognisable when the model runs on real quantum hardware?

The frozen hardware experiment

Processor ibm_marrakesh
IBM job da0q66no3ppc73alpe10
Logical width 56 qubits, with 44 occupied and 12 unoccupied modes
Live-transpiled circuit depth 271, 472 CZ gates
Comparison the same template at field scales 1 and 32
Observables four cell occupations plus total particle number
Mitigation measurement mitigation, twirling, and ZNE at noise factors 1, 3, and 5
QPU usage 14.7155 quantum seconds

What the hardware saw

Route RMSE vs ideal Direction cosine N(A) N(B)
Noise factor 1 0.105389 0.966469 39.9649 39.9868
IBM production ZNE 0.103770 0.938465 42.5025 42.4751
Linear zero-noise estimate 0.080154 0.974583 41.1930 41.2371

The sign pattern and direction of the four-cell response therefore remain clearly visible. In the first cell, the linear zero-noise point estimate moved from 0.255105 to 0.315258, closer to the ideal 0.376331. At the same time, the measured total particle number shows substantial noise relative to the ideal value of 44.

Why this is good news

  • The forced Hamiltonian change is genuinely part of the circuit, not a colour rendering added afterwards.
  • The hardware response points in the same direction as the exact model, with direction cosine between 0.966 and 0.975.
  • The linear ZNE point estimate is closer to the exact result.
  • Cell totals and the separate particle-number observable are internally consistent.

Why we remain cautious

The extrapolation uncertainties are large and the exponential zero-noise fit was invalid. Mitigation improvement is therefore not statistically demonstrated. The circuit also does not calculate a complete frequency-dependent optical spectrum. The colour #F9E29D comes from the classical optical layer used to calibrate the model parameters.

Claim boundary. This experiment shows that an empirically gold-colour-calibrated 56-qubit Hamiltonian retains a recognisable response pattern on IBM hardware. It does not establish ab-initio gold colour, a G0W0 correction, a direct quantum-hardware colour calculation, or quantum advantage.

The next scientific step

The forced route provides a fast, testable hardware model. The stricter route must independently determine what part of the 0.728883 eV shift can follow from quasiparticle corrections. A later hardware experiment can then compare the empirical Hamiltonian with a G0W0-constrained Hamiltonian under exactly the same protocol.

Sources and reproducibility

Project status: 16 August 2026. All numbers come from frozen local and published research artifacts.