Phase-Field Grover Machine for Physical Cost Minimisation
Teslia, Nikita Eduardovich · Zenodo (CERN European Organization for Nuclear Research) · 2025
This deposit contains the V10 report “Phase-Field Grover Machine for Physical Cost Minimisation” together with supplementary animated simulations (V10 sim GIF archive). V10 presents a single normalised complex phase-field substrate, based on a driven, weakly dissipative order parameter ψ(x,y,t)=Aeiφ\psi(x,y,t)=A e^{i\varphi}ψ(x,y,t)=Aeiφ, where diverse computational tasks are implemented by reshaping an effective energy landscape E[ψ]E[\psi]E[ψ] (oracle potentials and task-specific cost densities) while keeping the underlying field dynamics fixed. Instead of treating Grover’s algorithm as an abstract sequence of unitary gates on qubits, V10 embeds Grover-like behaviour into continuum dynamics: marked states correspond to local energetic preferences (oracle wells) and “diffusion” arises from spatial coupling. In the same hardware, V10 also demonstrates classical variational optimisation by coupling standard functionals to either ℜψ\Re\psiℜψ or ∣ψ∣|\psi|∣ψ∣. The result is a unified field-computing framework where “programming” is expressed primarily as an energy/cost functional rather than a discrete gate list. The report includes a structured description and representative frame sequences for the full experimental suite E1–E8: E1–E2: associative memory / resonant classification and robustness tests (heavy deletion, competing templates, phase breaks, vortices, strong phase noise, amplitude–phase conflict, fractal target). E3 & E5: Grover-like amplitude amplification (no-oracle control, single oracle, multiple oracles) and competition between alternative transport paths. E4: frustrated phase landscapes and guided transport via corridor-like potentials (“wave/path guidance”). E6: phase-label segmentation (quadrants) and conflict between incompatible segmentations (ring vs. quadrants). E7: variational PDE solving and optimisation (Poisson, Poisson with Grover-type weighting, anisotropic Poisson, Allen–Cahn, abstract cost minimisation). E8: maze solving interpreted as directional phase-guided transport through a static potential landscape. Supplementary material: the V10 sim archive provides one-to-one GIF animations for E1–E8, showing full temporal evolution beyond the representative frames in the PDF. Each file name corresponds directly to the experiment numbering for easy cross-reference.