Quantum Neural Networks - Computational Field Theory and Dynamics

Carlos Pedro Gonçalves

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper defines a two-neuron QRNN with F = U0 U1 and specifies U1, U0, and Ur; from these it derives that r=0 yields a fixed point and r=1 yields a 3-cycle for every state, i.e., |ψ(t+2)⟩ = |ψ(t−1)⟩, which implies F^3 = I4 for r=1. The candidate solution independently reaches the same conclusions by explicit matrix evaluation of U1, U0 at r ∈ {0,1}, constructing F, and verifying F^3 = I4 by its action on the computational basis. Hence, both are correct; the paper uses amplitude-iteration identities, while the model uses direct matrix multiplication and basis tracking. Key definitions and results appear in the paper’s equations (38)–(44) and the r=0,1 analysis with the 3-cycle (equations (56)–(58)) .

Referee report (LaTeX)

\textbf{Recommendation:} no revision

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The audited claim (fixed-point dynamics at r=0 and a 3-cycle at r=1 for the two-neuron QRNN) is rigorously supported by the paper’s amplitude-iteration analysis and independently confirmed by the model’s explicit matrix computation. The assumptions, basis ordering, and activation sequence are clearly specified in the paper, and the model adheres to them. The two proofs are methodologically distinct but fully consistent, leaving no gaps for these parameter choices.