24 gold spinor modes on IBM with ZNE-PEA

Part 8 · material-derived 24-qubit hardware

We now have more than a gold-inspired demonstration: 24 genuine spinor modes from the validated QE+SOC/Wannier90 chain were evolved as 24 qubits on IBM Kingston. The linear ZNE-PEA point estimate is closer to the exact reference, but its uncertainty is still too large to call this a statistically demonstrated correction.

What exactly was simulated?

Choice	Frozen protocol
Material basis	Two cells with twelve spinor Wannier modes each, derived from Quantum ESPRESSO with spin–orbit coupling and Wannier90: 24 occupation modes directly encoded in 24 qubits.
Electrons	22 electrons. The initial state is the Slater determinant of the 22 lowest eigenmodes of the effective one-particle Hamiltonian; no VQE was used.
Excitation	A local phase kick φ=0.25 on the left cell.
Dynamics	Real-time evolution to 0.10 femtoseconds.
Observable	The charge imbalance ΔN=N_left−N_right, and for the symmetry route its odd component under φ→−φ.

What “electron configuration” means here. This is not the isolated-atom notation [Xe]4f¹⁴5d¹⁰6s¹. In a solid, the electrons are described as occupied spinor bands. The 24 qubits are 24 possible occupation modes; the selected state contains 22 electrons and therefore two holes.

The classical bar before hardware

Mode order, source checksums, Hermiticity, particle number, active window, time step and the observable were frozen before submission. A direct 24×24 correlation-matrix calculation gives ΔN=0.1665042575; the independent fixed-particle statevector gives 0.1665042575 to roughly 4×10⁻¹⁵. For the exactly odd ±φ combination, the target is 0.1665032535.

The circuit passed the routing limits on ibm_kingston: all 24 problem modes were mapped onto 24 physical qubits of the 156-qubit processor. The Estimator route had depth 485 and 640 CZ gates.

The first hardware control failed physically

A matched Sampler run with −φ, 0 and +φ used 1024 shots per circuit. The measured odd response was −0.068359±0.06029, whereas the exact value is +0.166503. The mean measured particle number was about 18.58 rather than 22, and only 8–10% of the shots occupied the correct N=22 sector. Symmetry subtraction removed a static offset, but not the dominant particle leakage.

What ZNE with probabilistic error amplification changed

Exactly one preregistered EstimatorV2 job was then executed: d9u97qou5hac73agtv10, with PEA noise factors 1, 1.5 and 2, measurement mitigation and the default 1024 shots per evaluation. Exponential extrapolation was primary; a linear fit was frozen in advance as a secondary diagnostic.

Result	Odd response	Absolute point error	Interpretation
Exact	0.166503	0	Classical reference
PEA, exponential	0.245088±0.220665	0.078585	Primary fit; correct sign, broad interval
PEA, linear	0.208149±0.210538	0.041646	Secondary fit; best point estimate

Against the earlier Kingston/Fire Opal point estimate of 0.247891, the linear fit reduces absolute point error from 0.081387 to 0.041646, a nominal reduction of 48.8%. This is where “about 50% better” comes from. It is not a reduction in full-state error and it is not statistically significant: the linear estimate’s 95% interval is approximately [−0.205, 0.621]. The primary exponential fit barely improves the point error.

Did PEA restore the 22-electron state?

No. PEA extrapolates one expectation value to an estimated zero-noise limit. Estimator does not return a full bitstring distribution, so this job cannot show that the N=22 sector was restored. The earlier Sampler data instead demonstrate substantial particle-number leakage. One observable can have a good point estimate even when the complete output state is not correct.

What do we have, then?

A reproducible hardware execution of a 24-mode, spin–orbit-coupled gold Hamiltonian derived directly from QE/Wannier90.
An initial state with 22 occupied band modes, without VQE, and an exactly cross-checked local charge response.
A sign-consistent PEA result and a linear point estimate with 48.8% less point error than the frozen earlier Kingston comparison.
A clear negative diagnosis: at 1024 shots and this circuit depth, the hardware result is not accurate enough to confirm the electron configuration or response statistically.

The reproducibility bundle preserves configurations, QPY/QASM, backend mapping, job ID and checksums. The analysed PEA result file has SHA-256 ba147e56df6ede1c1f9afa64be811b364aaeff38ea9f029b0bac71b8abf487a8.

A systematic priority audit found no earlier publication with this exact combination of 24 used qubits, real gate-based hardware, elemental gold, real-time one-particle dynamics and a QE+SOC/Wannier90 Hamiltonian. The negative literature search must be repeated immediately before submitting a scientific paper; this Edukaizen page therefore makes no broad “first” claim.

Claim boundary. This result concerns a finite two-cell, independent-particle description of material-derived gold and one local observable at 0.10 fs. It does not predict the colour of gold, include fully correlated electron–electron dynamics, prove that hardware retained the 22-electron state, or demonstrate quantum advantage.

Sources and reproducibility

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