Q02: How can order finding be expressed through STP?

Working mathematical formulation

Give an end-to-end description of order finding using adaptive STP, with explicit encoding of the modular-arithmetic instance, measurement sequence, classical control, and readout. Seek a structural account of periodicity and interference beyond replacing each standard gate with a universal simulation.

Why this is interesting

The model can compute the answer in principle. The question is whether its language explains the algorithm and suggests a different implementation.

Explicit variants

A fiber-preserving arithmetic measurement
For $f(x)=a^x\bmod N$ , seek a native STP implementation on a specified logical encoding of the channel $\mathcal{D}_f(\lvert x\rangle\langle y\rvert)=\mathbf{1}_{f(x)=f(y)}\lvert x\rangle\langle y\rvert,$ preserving coherence within each fiber. Compare its cost with modular-arithmetic circuit compilation. A Fourier-type readout then needs an explicit real encoding or other coherent resource; Clebsch–Gordan coefficients alone do not implement modular arithmetic.

A place to start

Work through order finding for a small cyclic group and track which multiplicity-space quantities represent the periodic structure.

Related work

These works provide context and established results. They need not be the origin of this exact formulation.

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