We will formalize and experimentally verify how agent-environment feedback loops behave when the interaction channel exhibits quantum causal non-separability (process-matrix formalism) and Kochen-Specker contextuality. Building on our previous work we'll extend our density-operator reinforcement model to a higher-order map without predefined causal arrows develop a Bell-Kochen-Specker-type inequality tailored to sequential QAGI actions and implement a two-round quantum game on IBM-Q hardware where the QAGI chooses between entangled measurement settings. Our theoretical work indicates that non-classical causal structure may endow QAGI policies with greater decision-theoretic power than any causally-ordered classical or quantum Markov chain though our extension of KS to typical AGI procedures suggests limits to its effectiveness. This milestone addresses fundamental questions about how indefinite causal structures affect AGI reasoning capabilities and how contextuality can be leveraged as a resource for machine cognition.

Deliverables 1. Preprint with complete mathematical proofs of process-matrix extension for QAGI-MDPs and contextual value assignment theorems 2. Open-source simulation code implementing indefinite-causality channels for AGI 3. Codebase of experimental implementation enabling reproducibility 4. Formal theoretical results related to causal inequalities relevant to QAGI implementation 5. Comparative analysis of quantum vs. classical causal performance on adaptive bandit tasks 6. (Prospective) Simulated circuit designs for hardware implementation of contextual knowledge representation

$25,000 USD

Success Criteria 1. Demonstrate violation of our custom causal inequality on simulated quantum platform 2. Show statistically significant policy-efficiency uplift versus the best classical-causal baseline on adaptive bandit tasks 3. Prove formal theorems connecting quantum contextuality to specific AGI capabilities 4. Identify concrete hardware design requirements for preserving contextual properties in QAGI systems 5. Successfully implement at least one knowledge representation scheme that exploits quantum contextuality for improved reasoning

We will quantify the minimal work cost and entropy production necessary for cognitive updates within QAGI extending our previous Landauer-style bounds to fully coherent time-dependent control unitaries. By modeling the agent's belief-updating channel as a geodesic on the manifold of unitaries with entropy-weighted quantum Fisher metric we'll derive closed-form work functionals and prove dissipation lower bounds for any CPTP update. Our analysis will identify regimes where quantum coherence provides a thermodynamic advantage despite error-correction overhead. This builds on our existing simulations of quantum hardware substrates and incorporates the latest developments in quantum Bayesianism. This milestone addresses fundamental questions about thermodynamic limits on quantum AGI performance and how energetic constraints affect learning and inference (builds on related work we have on thermodynamics).

Deliverables 1. Peer-reviewed article with analytic derivations of work costs for QAGI cognitive operations 2. Comprehensive thermodynamic data tables for various quantum AGI architectures 3. Reproducible code notebooks calculating optimal control pulses under realistic noise 4. Formal mathematical proof of dissipation lower bounds for cognitive updates 5. Simulation results comparing thermodynamic efficiency across hardware platforms 6. Design principles for thermodynamically optimal QAGI architectures

$25,000 USD

Success Criteria 1. Demonstrate quantifiable thermodynamic advantage for at least one core AGI function using quantum coherence 2. Prove tight bounds on the minimal entropy production required for specific cognitive updates 3. Successfully model thermodynamic costs in simulated quantum hardware with realistic noise profiles 4. Identify at least one novel quantum learning algorithm that approaches the thermodynamic limits 5. Show improvement relative to the best-known classical reversible logic sequence for equivalent Bayesian evidence gain

We will establish tight upper and lower bounds on the quantum time and query complexity (Qq) of core cognitive subroutines essential to AGI including credit assignment hierarchical planning and causal graph inference. By formulating each subroutine as an oracle problem we'll derive Grover-type lower bounds and design matching amplitude-amplification algorithms. We'll adapt verification protocols to certify that a QAGI policy encoded in a PEPS tensor network has correctly compressed training data and map abstract algorithms to surface-code logical qubits to quantify real-world resource requirements. This milestone addresses which AGI-relevant problems show provable quantum advantages in computational or query complexity and how these advantages translate to practical implementations when accounting for error-correction overhead.

Deliverables 1. Formal complexity-theory manuscript suitable for mathematics/CS journal publication 2. Open-access code implementing algorithms with proven complexity advantages 3. Simulated quantum compiler plug-in emitting lattice-surgery schedules for benchmark circuits 4. Resource estimation tools calculating physical qubit requirements and runtime for QAGI operations 5. Catalog of AGI functions with rigorous quantum advantage proofs 6. Complexity-theoretic framework for evaluating quantum AGI proposals

$25,000 USD

Success Criteria 1. Prove asymptotic quantum advantage for at least three core AGI subroutines with full accounting for error correction overhead 2. Achieve an asymptotic complexity bound for causal-graph inference with total physical-qubit budget less than a scalar multiple of classical GPU baseline 3. Successfully implement at least one novel quantum algorithm specifically designed for an AGI-relevant task 4. Demonstrate lower query complexity for knowledge acquisition in simulated quantum environments 5. Create effective benchmarks comparing classical and quantum implementations of AGI functions

We will determine the fundamental performance envelope of AGI-level cognition when logical operations are mediated by fault-tolerant primitives. By integrating our transformer-style QAGI core into a rotated-surface-code stack we'll analyze how QEC constraints reshape agent architecture memory hierarchy and exploration strategies. We'll prove convergence conditions for policy-gradient ascent under fixed logical-cycle latency and design a hybrid stabilizer storage scheme that lowers logical memory cost while preserving code distance. Using hardware-in-the-loop testbeds with realistic correlated error spectra we'll run end-to-end agent-environment loops to evaluate real-world feasibility. This milestone addresses how error correction requirements constrain practical quantum AGI implementation and identifies which AGI functions maintain quantum advantages despite error correction overhead.

Deliverables 1. Academic paper on on architecture guidelines for fault-tolerant QAGI 2. Dataset of synthetic but physically-faithful error traces (subject to compute availability) 3. Dockerized simulation environment ready for adoption by peer laboratories (extending previous work on QDataSet) 4. Design specifications for hybrid memory-consolidation protocols 5. Formal proof of convergence conditions for stochastic control under QEC latency 6. Performance analysis of QAGI under realistic noise conditions with and without error correction

$25,000 USD

Success Criteria 1. Maintain average episodic reward within close proximity to the ideal-logical-gate model while operating at physical error rates 2. Design error correction protocols specifically optimized for AGI workloads 3. Demonstrate successful fault-tolerant implementation of at least two core AGI functions 4. Quantify resource overhead tradeoffs for error-corrected quantum AGI 5. Establish clear design principles for fault-tolerant quantum AGI that can guide future hardware development