Methods & honest assumptions (use in report)
Forward model. Reduced-order, calibrated displacement field u(x)=[A·ĝ − ε·x]·exp(−|x−c|²/2σ²), A=C·ρ·g·d·R(1−ν²)/E (ρg=0.0102 kPa/mm, R=60 mm, C=3.5 calibrated so typical settings give 5–10 mm surface shift), ε=0.012·mannitol dose, σ=0.55·Dcran+18 mm. It is not a patient-specific FEM; validate against FEM/iMRI data before clinical claims.
Sensing. K cortical markers in the craniotomy; per-axis noise σeff=√(σ²+pulsation²/2).
Inverse solvers. Displacement = Σ akφk(x) on 2n Gaussian RBF nodes. Ridge = exact regularised least squares. PQC = n-qubit state-vector simulation (RY + CZ-ring), trained with Adam and exact parameter-shift gradients. Classical simulator: no quantum hardware, no speed-up claim.
Metrics. TRE = |predicted − true| target position. FRE = RMS marker residual of the fit (fiducial registration error). Trials differ by marker layout and noise (seeded mulberry32).
Statistics used
Paired Wilcoxon signed-rank test (normal approximation, tie-corrected, n≥10), paired Cohen's d, 1000-resample bootstrap CI of the mean paired difference, Wilson 95% interval for the pass rate, Pearson r for FRE–TRE.
