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189 figures
Figure 1.1.1 — The Quantum Stack: From Physics to QAIS.

1.1.1

Figure 1.1.1 — The Quantum Stack: From Physics to QAIS.
Figure 1.2.1 — Dual System-Evaluation Lenses in QAIS.

1.2.1

Figure 1.2.1 — Dual System-Evaluation Lenses in QAIS.
Figure 1.2.2 — QAIS System-Layer Model with QALIS and CRQC–LLM Cross-Layer Roles.

1.2.2

Figure 1.2.2 — QAIS System-Layer Model with QALIS and CRQC–LLM Cross-Layer Roles.
Figure 1.2.3 — Cross-Layer Capability, Constraint, and Orchestration Flow in QAIS.

1.2.3

Figure 1.2.3 — Cross-Layer Capability, Constraint, and Orchestration Flow in QAIS.
Figure 1.2.4 — From QIS to QAIS as a System Discipline.

1.2.4

Figure 1.2.4 — From QIS to QAIS as a System Discipline.
Figure 1.3.1 — Classical vs Quantum Views of Information.

1.3.1

Figure 1.3.1 — Classical vs Quantum Views of Information.
Figure 1.4.1 — Bloch Sphere Representation.

1.4.1

Figure 1.4.1 — Bloch Sphere Representation.
Figure 1.4.2 — Entanglement as Nondecomposable Correlation.

1.4.2

Figure 1.4.2 — Entanglement as Nondecomposable Correlation.
Figure 1.4.3 — Entanglement as an Operational Resource in QAIS.

1.4.3

Figure 1.4.3 — Entanglement as an Operational Resource in QAIS.
Figure 1.4.4 — Core Metrics of Quantum Information.

1.4.4

Figure 1.4.4 — Core Metrics of Quantum Information.
Figure 2.2.1 — Representation and Encoding of Quantum States.

2.2.1

Figure 2.2.1 — Representation and Encoding of Quantum States.
Figure 2.3.1 — Copying and Observation as Rules in QAIS.

2.3.1

Figure 2.3.1 — Copying and Observation as Rules in QAIS.
Figure 2.4.1 — Entanglement and Correlation in QAIS.

2.4.1

Figure 2.4.1 — Entanglement and Correlation in QAIS.
Figure 2.5.1 — Contrasting Classical and Quantum Paradigms.

2.5.1

Figure 2.5.1 — Contrasting Classical and Quantum Paradigms.
Figure 2.6.1 — Classical and Quantum Computational Models.

2.6.1

Figure 2.6.1 — Classical and Quantum Computational Models.
Figure 2.7.1 — Classical Error Correction Using a Three-Bit Repetition Code.

2.7.1

Figure 2.7.1 — Classical Error Correction Using a Three-Bit Repetition Code.
Figure 2.7.2 — Quantum Error Correction (Conceptual Workflow).

2.7.2

Figure 2.7.2 — Quantum Error Correction (Conceptual Workflow).
Figure 2.8.1 — Symbolic Abstraction to Embodied Quantum Information.

2.8.1

Figure 2.8.1 — Symbolic Abstraction to Embodied Quantum Information.
Figure 2.9.1 — Bloch Sphere Representation of a Qubit.

2.9.1

Figure 2.9.1 — Bloch Sphere Representation of a Qubit.
Figure 2.9.2 — Bell State as Entangled Representation.

2.9.2

Figure 2.9.2 — Bell State as Entangled Representation.
Figure 2.9.3 — Formal Tools and Metrics in QAIS.

2.9.3

Figure 2.9.3 — Formal Tools and Metrics in QAIS.
Figure 2.9.4 — Operational Protocols in QAIS.

2.9.4

Figure 2.9.4 — Operational Protocols in QAIS.
Figure 2.9.5 — No-Go Theorems as Structural Rules in QAIS.

2.9.5

Figure 2.9.5 — No-Go Theorems as Structural Rules in QAIS.
Figure 2.9.6 — Constructive QAIS Alternatives to No-Go Theorems.

2.9.6

Figure 2.9.6 — Constructive QAIS Alternatives to No-Go Theorems.
Figure 2.11.1 — QAIS Operational Flow Model.

2.11.1

Figure 2.11.1 — QAIS Operational Flow Model.
Figure 3.3.1 — 1990s Algorithmic and Theoretical Advances in QAIS.

3.3.1

Figure 3.3.1 — 1990s Algorithmic and Theoretical Advances in QAIS.
Figure 3.3.2 — Quantum Repeaters as a Milestone in QAIS Evolution.

3.3.2

Figure 3.3.2 — Quantum Repeaters as a Milestone in QAIS Evolution.
Figure 3.3.3 — NISQ Architectures in QAIS.

3.3.3

Figure 3.3.3 — NISQ Architectures in QAIS.
Figure 3.3.4 — Policy and Ecosystem Evolution in QAIS.

3.3.4

Figure 3.3.4 — Policy and Ecosystem Evolution in QAIS.
Figure 3.4.1 — Classical vs Quantum Communication.

3.4.1

Figure 3.4.1 — Classical vs Quantum Communication.
Figure 3.4.2 — Communication Primitives in QAIS.

3.4.2

Figure 3.4.2 — Communication Primitives in QAIS.
Figure 3.4.3 — From Primitives to Secure QAIS Backbones.

3.4.3

Figure 3.4.3 — From Primitives to Secure QAIS Backbones.
Figure 3.5.1 — QAIS in Business and Industry.

3.5.1

Figure 3.5.1 — QAIS in Business and Industry.
Figure 3.5.2 — QAIS in Academic Research and Education.

3.5.2

Figure 3.5.2 — QAIS in Academic Research and Education.
Figure 3.5.3 — QAIS in Government and Policy.

3.5.3

Figure 3.5.3 — QAIS in Government and Policy.
Figure 3.6.1 — Applied Domains of Quantum Information Science.

3.6.1

Figure 3.6.1 — Applied Domains of Quantum Information Science.
Figure 3.6.2 — Hybrid Classical–Quantum Interface Loop.

3.6.2

Figure 3.6.2 — Hybrid Classical–Quantum Interface Loop.
Figure 3.7.1 — Barriers to QAIS Maturity.

3.7.1

Figure 3.7.1 — Barriers to QAIS Maturity.
Figure 3.7.2 — Physical and Engineering Constraints on QAIS.

3.7.2

Figure 3.7.2 — Physical and Engineering Constraints on QAIS.
Figure 3.7.3 — Infrastructure and Verification Barriers in QAIS.

3.7.3

Figure 3.7.3 — Infrastructure and Verification Barriers in QAIS.
Figure 3.8.1 — Glossary of Quantum Terms as Workforce Skill Domains.

3.8.1

Figure 3.8.1 — Glossary of Quantum Terms as Workforce Skill Domains.
Figure 3.8.2 — Foundational Domains of Quantum AI Systems Competency.

3.8.2

Figure 3.8.2 — Foundational Domains of Quantum AI Systems Competency.
Figure 3.8.3 — Computational Thinking and Tools in QAIS Practice.

3.8.3

Figure 3.8.3 — Computational Thinking and Tools in QAIS Practice.
Figure 3.8.4 — Interdisciplinary Skill Domains for QAIS Professionals.

3.8.4

Figure 3.8.4 — Interdisciplinary Skill Domains for QAIS Professionals.
Figure 3.8.5 — Workforce and Access Barriers in QAIS.

3.8.5

Figure 3.8.5 — Workforce and Access Barriers in QAIS.
Figure 3.8.6 — Interdependent Barriers in QAIS Deployment.

3.8.6

Figure 3.8.6 — Interdependent Barriers in QAIS Deployment.
Figure 3.9.1 — Three Layer Hybrid Architecture.

3.9.1

Figure 3.9.1 — Three Layer Hybrid Architecture.
Figure 3.9.2 — Deployable QAIS Modules.

3.9.2

Figure 3.9.2 — Deployable QAIS Modules.
Figure 3.9.3 — Classical vs Quantum AI Architectures.

3.9.3

Figure 3.9.3 — Classical vs Quantum AI Architectures.
Figure 3.9.4 — Bridging Classical and Quantum Layers in QAIS–AI Pipelines.

3.9.4

Figure 3.9.4 — Bridging Classical and Quantum Layers in QAIS–AI Pipelines.
Figure 3.9.5 — Hybrid QAIS–AI Stack Architecture.

3.9.5

Figure 3.9.5 — Hybrid QAIS–AI Stack Architecture.
Figure 3.9.6 — QALIS Hybrid Quantum–Classical Learning Workflow.

3.9.6

Figure 3.9.6 — QALIS Hybrid Quantum–Classical Learning Workflow.
Figure 3.9.7 — Quantum Data and Representational Power.

3.9.7

Figure 3.9.7 — Quantum Data and Representational Power.
Figure 3.9.8 — Security, Integrity, and Trust in Quantum Learning.

3.9.8

Figure 3.9.8 — Security, Integrity, and Trust in Quantum Learning.
Figure 3.9.9 — QAIS as the Disciplinary Scaffold of Hybrid Intelligence.

3.9.9

Figure 3.9.9 — QAIS as the Disciplinary Scaffold of Hybrid Intelligence.
Figure 3.9.10 — QAIS as the Logic of Next-Generation AI.

3.9.10

Figure 3.9.10 — QAIS as the Logic of Next-Generation AI.
Figure 4.3.1 — Classical Feature Normalization and Quantum Embedding.

4.3.1

Figure 4.3.1 — Classical Feature Normalization and Quantum Embedding.
Figure 4.3.2 — Shallow-Circuit Strategies for Amplitude-Based Embedding.

4.3.2

Figure 4.3.2 — Shallow-Circuit Strategies for Amplitude-Based Embedding.
Figure 4.3.3 — Hardware-Aware Template for Amplitude Encoding.

4.3.3

Figure 4.3.3 — Hardware-Aware Template for Amplitude Encoding.
Figure 4.3.4 — Two-Qubit Register Amplitude Mapping.

4.3.4

Figure 4.3.4 — Two-Qubit Register Amplitude Mapping.
Figure 4.3.5 — Amplitude Construction in Two-Qubit State Space.

4.3.5

Figure 4.3.5 — Amplitude Construction in Two-Qubit State Space.
Figure 4.4.1 — Angle Encoding through Parameterized Qubit Rotations.

4.4.1

Figure 4.4.1 — Angle Encoding through Parameterized Qubit Rotations.
Figure 4.4.2 — RX/RY/RZ Feature-to-Rotation Mapping.

4.4.2

Figure 4.4.2 — RX/RY/RZ Feature-to-Rotation Mapping.
Figure 4.4.3 — Classical Dense Layer vs Variational Quantum Layers.

4.4.3

Figure 4.4.3 — Classical Dense Layer vs Variational Quantum Layers.
Figure 4.5.1 — Binary String to Qubit Register Mapping.

4.5.1

Figure 4.5.1 — Binary String to Qubit Register Mapping.
Figure 4.5.2 — Linear Scaling vs Hybrid Integration Scheme.

4.5.2

Figure 4.5.2 — Linear Scaling vs Hybrid Integration Scheme.
Figure 4.5.3 — Basis Encoding in Hybrid Representation.

4.5.3

Figure 4.5.3 — Basis Encoding in Hybrid Representation.
Figure 4.6.1 — Structured Quantum Register with Role-Based Encoding.

4.6.1

Figure 4.6.1 — Structured Quantum Register with Role-Based Encoding.
Figure 4.6.2 — Layered Mixed-Encoding Circuit Architecture.

4.6.2

Figure 4.6.2 — Layered Mixed-Encoding Circuit Architecture.
Figure 4.6.3 — Hybrid Encoding Workflow Loop.

4.6.3

Figure 4.6.3 — Hybrid Encoding Workflow Loop.
Figure 4.7.1 — Classical-to-Hilbert Space Feature Mapping.

4.7.1

Figure 4.7.1 — Classical-to-Hilbert Space Feature Mapping.
Figure 4.7.2 — Rotational Geometry in Feature Space.

4.7.2

Figure 4.7.2 — Rotational Geometry in Feature Space.
Figure 4.7.3 — Decision Boundaries in Encoded State Space.

4.7.3

Figure 4.7.3 — Decision Boundaries in Encoded State Space.
Figure 4.7.4 — Kernel Similarity via Inner Product Geometry.

4.7.4

Figure 4.7.4 — Kernel Similarity via Inner Product Geometry.
Figure 4.8.1 — Circuit Depth Comparison Across Encodings.

4.8.1

Figure 4.8.1 — Circuit Depth Comparison Across Encodings.
Figure 4.8.2 — Noise-Resilient Encoding Design.

4.8.2

Figure 4.8.2 — Noise-Resilient Encoding Design.
Figure 4.9.1 — Ideal vs Hardware-Constrained Encoding.

4.9.1

Figure 4.9.1 — Ideal vs Hardware-Constrained Encoding.
Figure 4.9.2 — Encoding as Stack-Level Architectural Constraint.

4.9.2

Figure 4.9.2 — Encoding as Stack-Level Architectural Constraint.
Figure 5.2.1 — Reversible Quantum Operations Using Controlled and Unitary Gates.

5.2.1

Figure 5.2.1 — Reversible Quantum Operations Using Controlled and Unitary Gates.
Figure 5.3.1 — Conditional Evaluation with Multi-Controlled Circuits.

5.3.1

Figure 5.3.1 — Conditional Evaluation with Multi-Controlled Circuits.
Figure 5.4.1— Visualizing Phase-Based Logical Marking in Superposition.

5.4.1

Figure 5.4.1— Visualizing Phase-Based Logical Marking in Superposition.
Figure 5.5.1 — Amplitude Amplification Through Interference.

5.5.1

Figure 5.5.1 — Amplitude Amplification Through Interference.
Figure 5.6.1 — Distributed Agents Sharing an Entangled State.

5.6.1

Figure 5.6.1 — Distributed Agents Sharing an Entangled State.
Figure 5.6.2 — Bell Test Circuit Demonstrating Logical Correlation.

5.6.2

Figure 5.6.2 — Bell Test Circuit Demonstrating Logical Correlation.
Figure 5.6.3 — Local Operations on a Shared Entangled State.

5.6.3

Figure 5.6.3 — Local Operations on a Shared Entangled State.
Figure 5.7.1 — Quantum Reasoning Loop with Collapse Feedback.

5.7.1

Figure 5.7.1 — Quantum Reasoning Loop with Collapse Feedback.
Figure 5.7.2 — Hybrid Quantum–Classical Feedback Graph.

5.7.2

Figure 5.7.2 — Hybrid Quantum–Classical Feedback Graph.
Figure 5.8.1 — Variational Feedback Loop for Quantum Reasoning.

5.8.1

Figure 5.8.1 — Variational Feedback Loop for Quantum Reasoning.
Figure 5.9.1 — Controlled Operations for Multi-Stage Quantum Inference.

5.9.1

Figure 5.9.1 — Controlled Operations for Multi-Stage Quantum Inference.
Figure 5.10.1 — Quantum Rule Evaluation Circuit.

5.10.1

Figure 5.10.1 — Quantum Rule Evaluation Circuit.
Figure 5.10.2 — Quantum Robot with Adaptive Reasoning Loop.

5.10.2

Figure 5.10.2 — Quantum Robot with Adaptive Reasoning Loop.
Figure 5.10.3 — Quantum Belief Register and Update Flow.

5.10.3

Figure 5.10.3 — Quantum Belief Register and Update Flow.
Figure 6.3.1 — Amplitude Encoding vs Classical State Representation.

6.3.1

Figure 6.3.1 — Amplitude Encoding vs Classical State Representation.
Figure 6.4.1 — Classical vs Grover Search Complexity.

6.4.1

Figure 6.4.1 — Classical vs Grover Search Complexity.
Figure 6.4.2 — QFT-Based Period Finding in Shor’s Algorithm.

6.4.2

Figure 6.4.2 — QFT-Based Period Finding in Shor’s Algorithm.
Figure 6.5.1 — QAOA Hybrid Optimization Loop.

6.5.1

Figure 6.5.1 — QAOA Hybrid Optimization Loop.
Figure 6.6.1 — QNN Layered Architecture with Entanglement.

6.6.1

Figure 6.6.1 — QNN Layered Architecture with Entanglement.
Figure 6.7.1 — Graph Partitioning with QAOA.

6.7.1

Figure 6.7.1 — Graph Partitioning with QAOA.
Figure 6.7.2 — Quantum State Overlap Classification.

6.7.2

Figure 6.7.2 — Quantum State Overlap Classification.
Figure 6.8.1 — Task-Specific Advantage Validation Model.

6.8.1

Figure 6.8.1 — Task-Specific Advantage Validation Model.
Figure 7.3.1 — Parameterized Quantum Circuit and Hybrid Optimization.

7.3.1

Figure 7.3.1 — Parameterized Quantum Circuit and Hybrid Optimization.
Figure 7.3.2 — Visualizing Encoding Schemes in Quantum Circuits.

7.3.2

Figure 7.3.2 — Visualizing Encoding Schemes in Quantum Circuits.
Figure 7.4.1 — Training Workflow for Hybrid QML Models.

7.4.1

Figure 7.4.1 — Training Workflow for Hybrid QML Models.
Figure 7.4.2 — Gradient Estimation with Parameter Shift Rule.

7.4.2

Figure 7.4.2 — Gradient Estimation with Parameter Shift Rule.
Figure 7.5.1 — Trade-off Between Circuit Depth and Fidelity.

7.5.1

Figure 7.5.1 — Trade-off Between Circuit Depth and Fidelity.
Figure 7.5.2 — Fidelity Loss in Deep Quantum Circuits.

7.5.2

Figure 7.5.2 — Fidelity Loss in Deep Quantum Circuits.
Figure 7.6.1 — QNN Layered Structure for QAI Learning.

7.6.1

Figure 7.6.1 — QNN Layered Structure for QAI Learning.
Figure 7.6.2 — Barren Plateaus and Gradient Collapse in QNNs.

7.6.2

Figure 7.6.2 — Barren Plateaus and Gradient Collapse in QNNs.
Figure 7.7.1 — Quantum Kernel Estimation for QSVM Classification.

7.7.1

Figure 7.7.1 — Quantum Kernel Estimation for QSVM Classification.
Figure 7.8.1 — Architecture of a Hybrid Quantum GAN.

7.8.1

Figure 7.8.1 — Architecture of a Hybrid Quantum GAN.
Figure 7.8.2 — QAIS Layer-5 Quantum ML Architecture Taxonomy.

7.8.2

Figure 7.8.2 — QAIS Layer-5 Quantum ML Architecture Taxonomy.
Figure 7.10.1 — Entanglement in Multi-Agent Quantum Learning.

7.10.1

Figure 7.10.1 — Entanglement in Multi-Agent Quantum Learning.
Figure 8.1.1 — Classical vs Quantum Optimization Pipelines.

8.1.1

Figure 8.1.1 — Classical vs Quantum Optimization Pipelines.
Figure 8.1.2 — Cost-Function-to-Hamiltonian Mapping.

8.1.2

Figure 8.1.2 — Cost-Function-to-Hamiltonian Mapping.
Figure 8.2.1 — Translating Classical Problems to Quantum Hamiltonians.

8.2.1

Figure 8.2.1 — Translating Classical Problems to Quantum Hamiltonians.
Figure 8.2.2 — Quantum Cost Evaluation.

8.2.2

Figure 8.2.2 — Quantum Cost Evaluation.
Figure 8.3.1 — Layered Cost-Mixer Circuit in QAOA.

8.3.1

Figure 8.3.1 — Layered Cost-Mixer Circuit in QAOA.
Figure 8.3.2 — VQE Optimization Cycle.

8.3.2

Figure 8.3.2 — VQE Optimization Cycle.
Figure 8.4.1 — Layered Circuit in QAOA.

8.4.1

Figure 8.4.1 — Layered Circuit in QAOA.
Figure 8.4.2 — Parameter Shift Rule.

8.4.2

Figure 8.4.2 — Parameter Shift Rule.
Figure 8.5.1 — QAOA for Resource Allocation.

8.5.1

Figure 8.5.1 — QAOA for Resource Allocation.
Figure 8.5.2 — Quantum Clustering using QAOA.

8.5.2

Figure 8.5.2 — Quantum Clustering using QAOA.
Figure 8.5.3 — Hyperparameter Search with VQE.

8.5.3

Figure 8.5.3 — Hyperparameter Search with VQE.
Figure 8.6.1 — Noise and Error in Quantum Circuits.

8.6.1

Figure 8.6.1 — Noise and Error in Quantum Circuits.
Figure 8.6.2 — Complexity vs Trainability in Ansatz Design.

8.6.2

Figure 8.6.2 — Complexity vs Trainability in Ansatz Design.
Figure 8.6.3 — Emerging Research Areas in Quantum AI.

8.6.3

Figure 8.6.3 — Emerging Research Areas in Quantum AI.
Figure 9.1.1 — Classical vs Quantum Optimization Landscapes.

9.1.1

Figure 9.1.1 — Classical vs Quantum Optimization Landscapes.
Figure 9.2.1 — Classical Bits vs Quantum Qubits.

9.2.1

Figure 9.2.1 — Classical Bits vs Quantum Qubits.
Figure 9.2.2 — Classical Probabilities vs Quantum Amplitudes.

9.2.2

Figure 9.2.2 — Classical Probabilities vs Quantum Amplitudes.
Figure 9.3.1 — Pure vs Mixed Quantum States and Their Entropy.

9.3.1

Figure 9.3.1 — Pure vs Mixed Quantum States and Their Entropy.
Figure 9.3.2 — Visualizing Quantum Correlation.

9.3.2

Figure 9.3.2 — Visualizing Quantum Correlation.
Figure 9.4.1 — Fidelity vs Trace Distance During Quantum Learning.

9.4.1

Figure 9.4.1 — Fidelity vs Trace Distance During Quantum Learning.
Figure 9.5.1 — Finite-Dimensional Illustration of Quantum-State Subspace Truncation.

9.5.1

Figure 9.5.1 — Finite-Dimensional Illustration of Quantum-State Subspace Truncation.
Figure 9.5.2 — Practical Compression Pipeline for QML.

9.5.2

Figure 9.5.2 — Practical Compression Pipeline for QML.
Figure 9.6.1 — Kraus Mathematical Channel Decomposition.

9.6.1

Figure 9.6.1 — Kraus Mathematical Channel Decomposition.
Figure 9.6.2 — Operational Noise Pathways in a Quantum Channel.

9.6.2

Figure 9.6.2 — Operational Noise Pathways in a Quantum Channel.
Figure 9.6.3 — Noise-Induced Learning Divergence.

9.6.3

Figure 9.6.3 — Noise-Induced Learning Divergence.
Figure 9.7.1 — Fidelity-Guided Pattern Recognition in QML.

9.7.1

Figure 9.7.1 — Fidelity-Guided Pattern Recognition in QML.
Figure 9.7.2 — Variational Learning Process with QIT-Based Evaluation.

9.7.2

Figure 9.7.2 — Variational Learning Process with QIT-Based Evaluation.
Figure 10.2.1 — Entanglement Distribution Across Quantum Nodes.

10.2.1

Figure 10.2.1 — Entanglement Distribution Across Quantum Nodes.
Figure 10.2.2 — Quantum Teleportation Between Distributed AI Agents.

10.2.2

Figure 10.2.2 — Quantum Teleportation Between Distributed AI Agents.
Figure 10.3.1 — Proposed Quantum Networking Stack with AI Integration.

10.3.1

Figure 10.3.1 — Proposed Quantum Networking Stack with AI Integration.
Figure 10.3.2 — Protocol Stack for Entanglement Resource Management.

10.3.2

Figure 10.3.2 — Protocol Stack for Entanglement Resource Management.
Figure 10.3.3 — Quantum Key Distribution in Trusted AI Systems.

10.3.3

Figure 10.3.3 — Quantum Key Distribution in Trusted AI Systems.
Figure 10.3.4 — Trusted Nodes and QRNG Integration for AI Coordination.

10.3.4

Figure 10.3.4 — Trusted Nodes and QRNG Integration for AI Coordination.
Figure 10.4.1 — Quantum Entanglement Handoff in Multi-Agent Routing.

10.4.1

Figure 10.4.1 — Quantum Entanglement Handoff in Multi-Agent Routing.
Figure 10.4.2 — Reinforcement in Entangled AI Learning Systems.

10.4.2

Figure 10.4.2 — Reinforcement in Entangled AI Learning Systems.
Figure 10.5.1 — Persistent Quantum Memory in Distributed AI.

10.5.1

Figure 10.5.1 — Persistent Quantum Memory in Distributed AI.
Figure 10.5.2 — Lifelong Memory Encoding via Qudit Networks.

10.5.2

Figure 10.5.2 — Lifelong Memory Encoding via Qudit Networks.
Figure 10.6.1 — Adaptive Entanglement Routing via Telemetry Feedback.

10.6.1

Figure 10.6.1 — Adaptive Entanglement Routing via Telemetry Feedback.
Figure 10.6.2 — Self-Healing Protocols for Quantum-AI Subnets.

10.6.2

Figure 10.6.2 — Self-Healing Protocols for Quantum-AI Subnets.
Figure 10.7.1 — Entangled Authentication and Identity in QAIS.

10.7.1

Figure 10.7.1 — Entangled Authentication and Identity in QAIS.
Figure 10.7.2 — Quantum Access Control via Entanglement.

10.7.2

Figure 10.7.2 — Quantum Access Control via Entanglement.
Figure 11.2.1 — Basic Architecture of a Quantum Sensing System.

11.2.1

Figure 11.2.1 — Basic Architecture of a Quantum Sensing System.
Figure 11.2.2 — Classical vs Quantum Sensing Regimes.

11.2.2

Figure 11.2.2 — Classical vs Quantum Sensing Regimes.
Figure 11.2.3 — Parameter Encoding into Quantum States.

11.2.3

Figure 11.2.3 — Parameter Encoding into Quantum States.
Figure 11.2.4 — Scaling Behavior of Estimation Uncertainty.

11.2.4

Figure 11.2.4 — Scaling Behavior of Estimation Uncertainty.
Figure 11.3.1 — Topology of a Distributed Quantum Sensing Network.

11.3.1

Figure 11.3.1 — Topology of a Distributed Quantum Sensing Network.
Figure 11.3.2 — Precision Gain from Quantum Network Coordination.

11.3.2

Figure 11.3.2 — Precision Gain from Quantum Network Coordination.
Figure 11.4.1 — Closed-Loop Quantum Sensing Control.

11.4.1

Figure 11.4.1 — Closed-Loop Quantum Sensing Control.
Figure 11.4.2 — Reinforcement Learning in Quantum Estimation.

11.4.2

Figure 11.4.2 — Reinforcement Learning in Quantum Estimation.
Figure 11.4.3 — Quantum-Enhanced Perception-to-Action Pipeline.

11.4.3

Figure 11.4.3 — Quantum-Enhanced Perception-to-Action Pipeline.
Figure 11.4.4 — Accuracy vs Latency: Quantum vs Classical.

11.4.4

Figure 11.4.4 — Accuracy vs Latency: Quantum vs Classical.
Figure 11.5.1 — Intelligent Quantum Sensing Architecture.

11.5.1

Figure 11.5.1 — Intelligent Quantum Sensing Architecture.
Figure 11.5.2 — Deployment Topologies for Intelligent Quantum Sensing.

11.5.2

Figure 11.5.2 — Deployment Topologies for Intelligent Quantum Sensing.
Figure 11.6.1 — Key Challenge Domains in Intelligent Quantum Sensing.

11.6.1

Figure 11.6.1 — Key Challenge Domains in Intelligent Quantum Sensing.
Figure 11.6.2 — Roadmap for Intelligent Quantum Sensing Technologies.

11.6.2

Figure 11.6.2 — Roadmap for Intelligent Quantum Sensing Technologies.
Figure 12.1.1 — QAIS Closed-Loop Execution and Propagation.

12.1.1

Figure 12.1.1 — QAIS Closed-Loop Execution and Propagation.
Figure 12.2.1 — Information Stability and State Similarity in QAIS Systems.

12.2.1

Figure 12.2.1 — Information Stability and State Similarity in QAIS Systems.
Figure 12.2.2 — Propagation Dynamics Across Closed-Loop QAIS Layers.

12.2.2

Figure 12.2.2 — Propagation Dynamics Across Closed-Loop QAIS Layers.
Figure 12.3.1 — Cross-Domain Propagation in CRQC–LLM Systems.

12.3.1

Figure 12.3.1 — Cross-Domain Propagation in CRQC–LLM Systems.
Figure 12.3.2 — Hybrid Quantum–Classical Propagation Paths.

12.3.2

Figure 12.3.2 — Hybrid Quantum–Classical Propagation Paths.
Figure 12.4.1 — Quantum Phase Estimation Circuit for qPCA.

12.4.1

Figure 12.4.1 — Quantum Phase Estimation Circuit for qPCA.
Figure 12.4.2 — Eigenvalue Filtering in qPCA-Based Feature Compression.

12.4.2

Figure 12.4.2 — Eigenvalue Filtering in qPCA-Based Feature Compression.
Figure 12.5.1 — Observable-Driven Quantum Feature Map.

12.5.1

Figure 12.5.1 — Observable-Driven Quantum Feature Map.
Figure 12.6.1 — Layered Circuit for Quantum Latent Compression.

12.6.1

Figure 12.6.1 — Layered Circuit for Quantum Latent Compression.
Figure 12.6.2 — Quantum Autoencoder for Feature Compression.

12.6.2

Figure 12.6.2 — Quantum Autoencoder for Feature Compression.
Figure 12.7.1 — Separability and Propagation in Hilbert Space.

12.7.1

Figure 12.7.1 — Separability and Propagation in Hilbert Space.
Figure 12.8.1 — Postselection and Propagation Control in QAIS Systems.

12.8.1

Figure 12.8.1 — Postselection and Propagation Control in QAIS Systems.
Figure 12.9.1 — Fidelity Matrix for Quantum Feature Similarity.

12.9.1

Figure 12.9.1 — Fidelity Matrix for Quantum Feature Similarity.
Figure 12.10.1 — Closed-Loop QAIS Integration and Propagation Surfaces.

12.10.1

Figure 12.10.1 — Closed-Loop QAIS Integration and Propagation Surfaces.
Figure 12.11.1 — Governed vs Unbounded Propagation in QAIS Systems.

12.11.1

Figure 12.11.1 — Governed vs Unbounded Propagation in QAIS Systems.
Figure 13.1.1 — Embedded vs Quantum-Native Architectures.

13.1.1

Figure 13.1.1 — Embedded vs Quantum-Native Architectures.
Figure 13.2.1 — Scaling: Embedded vs Quantum-Native Integration.

13.2.1

Figure 13.2.1 — Scaling: Embedded vs Quantum-Native Integration.
Figure 13.3.1 — Feedback Propagation in Classical vs Quantum Generative Systems.

13.3.1

Figure 13.3.1 — Feedback Propagation in Classical vs Quantum Generative Systems.
Figure 13.5.1 — Governance as Propagation Control.

13.5.1

Figure 13.5.1 — Governance as Propagation Control.
Figure 13.6.1 — Representation as a Control Surface.

13.6.1

Figure 13.6.1 — Representation as a Control Surface.
Figure F.1 — Canonical Seven-Layer QAIS Quantum Stack.

F.1

Figure F.1 — Canonical Seven-Layer QAIS Quantum Stack.
Figure F.2 — Illustrative Hybrid Quantum–Classical Iterative Workflow.

F.2

Figure F.2 — Illustrative Hybrid Quantum–Classical Iterative Workflow.