The road to quantum advantage for gold

Part 7 · research roadmap

Quantum advantage for gold requires more than a large qubit count or a completed hardware job. Quantum and classical routes must solve the same physical task at the same accuracy under an honest timing protocol.

The active-space ladder

Width Role Status
4 qubits Exact one-hole reduction of 12 material-derived spinor modes Executed on hardware; classically easy.
24 qubits Four-site interacting transport control model Exact/observable validation and hardware execution; still Au-inspired.
48 qubits Complete 5d+6s space on four Au sites Resource candidate; Wannier labels, matrix elements and interactions remain to be frozen.
56 qubits 5d+6s plus an effective 6p optical band Recommended candidate; the present shallow circuit proxy still uses synthetic coefficients.
60 qubits Larger effective transport benchmark or five-site 5d+6s model The generic route was too deep: depth 3108 and 4944 CZ gates in the best attempt.
72 qubits Complete local 5d+6s+6p optical space Long-term target, not a hardware claim.

When may we say “advantage”?

  1. Freeze one complete task, such as a spectral or transport observable with a stated error tolerance.
  2. Import the material Hamiltonian, dipoles and screened interactions without fitting the colour.
  3. Show an overlap regime in which quantum and the strongest classical methods agree.
  4. Measure QPU active time, shots, compilation, mitigation and failed attempts under one protocol.
  5. Compare against symmetry-aware exact methods, Krylov methods, tensor networks and particle-hole methods.
  6. Only then scale beyond the classical range while retaining an internal verification strategy.

The present conclusion

The 24-qubit results demonstrate technical feasibility and a useful mitigation comparison. They do not demonstrate quantum advantage. A possible first boundary lies around 48–60 qubits, but “possible” is neither an extrapolation nor a claim. The 56-qubit route is physically more interesting because it adds an explicit optical channel, while the 60-qubit routing test shows why qubit count without depth control means little.

Outlook: the value of this roadmap is that the next step is falsifiable. A material-derived 48/56-qubit Hamiltonian must first pass small classical overlap tests and hardware-routing gates. Failure to pass them would also be a scientific result.
Claim boundary. Quantum advantage for gold has not been realised. The current evidence defines a credible route and the experiments required to justify—or reject—such a claim later.

Sources and reproducibility

Project status: 8 August 2026. Numerical values come from the frozen local research artifacts; the original claim boundaries are deliberately preserved.