Quantum deliberating machines

TL;DR

This work introduces and analyzes a toy model of a quantum physical device capable of internal, self-referential deliberation, and frames the proposed model as a plausible setting for exploring how such devices may maintain multiple alternatives in parallel, while performing an internal decision-making process through coherent branching, entanglement, adaptive policy updates, and policy-driven self-modifying unitary dynamics.

Abstract

Within the familiar circuit-based quantum computational setting, we introduce and analyze a toy model of a quantum physical device capable of internal, self-referential deliberation. The key idea is to represent ``deliberation'' as a coherent iterative branching process, in which competing branch-dependent system evolutions are maintained in superposition, with additional control and memory registers recording branch histories, and the policy register adaptively biasing subsequent development. We provide explicit quantum circuit realizations and carry out detailed step-by-step derivations of the entangled control--memory--system--policy dynamics. We carefully distinguish between internally adaptive and internally reinforced deliberations, proposing the architectures for both, and briefly discuss categorical and controlled--Stinespring reformulations, as well as their conceptual implications. The primary construction models a memory-driven deliberation where the policy update depends on which actions were taken, not on their results. We also present a simple extension that allows for minimalistic, outcome-driven policy updates, implementing a coherent feedback loop that steers the system toward a target state regardless of initial branch-dependent evolution. This loop can be interpreted as a quantum autopilot or search-and-rescue mechanism, illustrating how a device can autonomously correct and optimize its internal strategy in superposition. Finally, we briefly consider various implementations of a dialogue that may take place between two deliberating machines. Taken together, this frames the proposed model as a plausible setting for exploring how such devices may maintain multiple alternatives in parallel, while performing an internal decision-making process through coherent branching, entanglement, adaptive policy updates, and policy-driven self-modifying unitary dynamics.

Figures (14)

• Figure 1: Controlled-unitary evolution: $C$ selects between $U_0$ or $U_1$ on $S$, creating a coherent superposition of process paths.
• Figure 2: Memory recording: $M$ entangled with $C$ to record the branch without measurement.
• Figure 3: Quantum policy update, $V_{\rm update}$: $P$ is updated conditionally on memory $M$.
• Figure 4: Policy-controlled feedback $F_{\rm feedback}$ (performed before policy update): $S$ undergoes additional unitary evolution, conditioned on policy $P$.
• Figure 5: Overview of the QDM. Control qubit $C$ determines the superposed unitary applied to system $S$, memory $M$ records branch information, and policy $P$ adapts conditionally. Dashed arrow indicates possible feedback in iterative evolution.