Relativistic gold on a quantum computer

Public research series · August 2026

Why is gold yellow, what role does relativity play, and what can a quantum computer genuinely add? This series follows one auditable route from measured gold optics and relativistic band structure to Qiskit circuits on 4 and 24 qubits.

The central conclusion: the project is quantum-first in design but hybrid in its evidence. Classical electronic-structure calculations define the material model, exact calculations validate the small regimes, and quantum hardware executes the selected dynamics.

What has already been achieved

4 qubitsMaterial-derived hardware experiment

An accepted QE+SOC/Wannier90 Hamiltonian with 12 spinor modes and 11 electrons reduces exactly to a 12-dimensional one-hole space.

0.8581Best Hellinger fidelity

Measured on IBM Kingston after M3 readout correction and exact postselection onto the allowed compact space. This is a hardware smoke test, not a prediction of gold’s colour.

24 qubitsMaterial-derived dynamics

All 24 spinor modes come from the QE+SOC/Wannier90 chain. The occupied-band state evolved on IBM Kingston without VQE.

The evidence map

Layer	Status	What the evidence supports	What it does not yet support
Measured optics	Reference	Olmon data combined with CIE colour conversion reproduce the known reflectance edge and gold-like colour.	This is not a prediction from the quantum circuit.
QE+SOC → Wannier90	Validated for the compact one-particle route	The 12 spinor modes are material-derived and checked on the relevant grid.	No complete interacting Brillouin-zone optical calculation yet.
4-qubit IBM	Executed	Real QPU execution of the exact one-hole reduction, including noise analysis.	No many-body or quantum advantage claim.
24-qubit gold	Material-derived and executed on hardware	A frozen charge response of 24 genuine spinor modes was exactly validated, routed and measured with 24 physical qubits.	The PEA improvement is not statistically significant and does not reconstruct the full electronic state.
48–72 qubits	Research roadmap	The active-space ladder and acceptance tests are explicit.	No hardware or advantage result.

Why this series exists

A 2025 paper attempted to combine DFT and VQE for metal clusters. The aluminium calculations succeeded, but the gold route encountered memory limits, open-shell handling and missing relativistic support. That negative result matters because it identifies a formulation that asks too much at once.

Our route begins with a narrower question. If the initial state and Hamiltonian are known and the goal is real-time evolution, a VQE minimum does not need to be found. Symmetry and particle number can sometimes compress the relevant Hilbert space exactly. For the 24-qubit step we also restrict the claim itself: one local observable at one short time.

Reading order

The nine parts progress from physics to hardware and finish with the forced 56-qubit experiment on IBM Marrakesh, including what mitigation can and cannot say about the electrons. Every part includes its sources and claim boundary.

Sources and reproducibility

Project status: 13 August 2026. Numerical values come from the frozen local research artifacts; the original claim boundaries are deliberately preserved.