The Patterns of Cognition (PoC) framework casts diverse AGI algorithms—probabilistic logic networks, evolutionary program learning, deep Q-learning, attention focusing and more—as approximate stochastic dynamic programs on typed metagraphs. Each algorithm is implemented by a chronomorphism: an unfold functor that generates a tree of candidate states and a fold functor that collapses this tree using a preorder, forming a Galois connection that monotonically improves solution quality. Here we explain how to port this framework to the quantum computing domain, obtaining a similar unified treatment of AGI algorithms applicable to quantum implementation. The approach taken leverages the facts that in continuous time the chronomorphism operator approximates the Hamilton–Jacobi–Bellman (HJB) equation; whereas a logarithmic action \(\rightarrow \) wavefunction transform, plus Wick rotation for diffusive noise, turns the HJB into the Schrödinger or heat equation. Thus every PoC chronomorphism lifts to a sparse Hamiltonian \( H_{\textrm{eff}} = H_C + H_R \) whose off-diagonal block \(H_C\) encodes combinatory expansion and whose diagonal block \(H_R\) encodes evaluation phases. Second-order Trotter or qubitization then realizes the small-time propagator \( U(\Delta t) \approx e^{-iH_R\Delta t/2} e^{-iH_C\Delta t} e^{-iH_R\Delta t/2} \) in \(\widetilde{O}(d\,\Vert H_{\textrm{eff}}\Vert \, t)\) fault-tolerant gates, giving quadratic speed-ups in, for instance, batch size, action branching and fitness estimation. A rough resource analysis shows that a hypothetical next-generation Dirac3+ 10k-qubit machine would likely scale quite favorably to thousand-agent workloads.  The sequel paper elaborates how this mechanism can be leveraged for a number of the key AI algorithms involved in the OpenCog Hyperon architecture—illustrating that the given mechanisms can be considered as a general-purpose scalable control loop for Hyperon-style quantum AGI systems.