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Combinatorial Optimization with QAOA | Quantum Computing Hub

The Quantum Approximate Optimization Algorithm (QAOA) is a leading NISQ-era algorithm for combinatorial optimization. This guide covers QAOA circuit design for MaxCut, TSP, portfolio optimization, and CSPs, with parameter optimization strategies and NISQ-era limitations. 1. QAOA Fundamentals 1.1 Theory Overview # qaoa_theory.py # QAOA solves: max_x C(x) where C: {0,1}^n → ℝ # # Hamiltonian formulation: # H_C = Σ C_i Z_i + Σ C_ij Z_i Z_j + ... (problem Hamiltonian) # H_M = Σ X_i (mixer Hamiltonian) # # QAOA state: |ψ(γ, β)⟩ = ∏_{p=1}^P e^{-iβ_p H_M} e^{-iγ_p H_C} |+⟩^{⊗n} # # Optimal parameters (γ*, β*) = argmax ⟨ψ(γ, β)| H_C |ψ(γ, β)⟩ # # As P → ∞, QAOA finds exact optimum (adiabatic theorem) # For finite P: approximation ratio depends on problem structure import numpy as np from qiskit import QuantumCircuit from qiskit.circuit import Parameter # QAOA ansatz construction def qaoa_ansatz(n_qubits, p, H_C, H_M): """Construct QAOA circuit for P layers""...

IoT Protocols Compared: MQTT, CoAP, HTTP/2, WebSocket - Performance, Overhead, and Use Cases | Embedded Systems Hub

Introduction Technical comparison of MQTT 3.1.1/5.0, CoAP, HTTP/2, and WebSocket for IoT: message overhead, QoS, connection patterns, and protocol selection matrix. This article provides a comprehensive technical deep-dive into the subject, covering theoretical foundations, practical implementation strategies, and real-world engineering trade-offs encountered in production embedded systems. Core Concepts Fundamental Principles Understanding the fundamental principles is essential before diving into implementation. This section covers the theoretical underpinnings that drive design decisions in embedded systems engineering. Key Terminology MCU/MPU: Microcontroller Unit / Microprocessor Unit - the compute engine RTOS: Real-Time Operating System - deterministic task scheduling HAL: Hardware Abstraction Layer - portable hardware interface BSP: Board Support Package - hardware-specific initialization OTA: Over-The-Air - remote firmware updates System Constraints Embedded systems operate und...

MLOps Pipeline Design Patterns: From Experimentation to Production | AI/ML Engineering Hub

Introduction Complete guide to ML pipeline architecture patterns: DAG-based orchestration, feature stores, model registries, CI/CD for ML, and production monitoring strategies. This article provides a comprehensive technical deep-dive into the subject, covering theoretical foundations, practical implementation strategies, and real-world engineering trade-offs encountered in production AI/ML systems. Core Concepts Fundamental Principles Understanding the fundamental principles is essential before diving into implementation. This section covers the theoretical underpinnings that drive design decisions in AI/ML engineering. Key Terminology MLOps: Machine Learning Operations - practices for reliable ML model deployment LLMOps: LLM Operations - specialized MLOps for large language models Feature Store: Centralized repository for ML features with online/offline serving Model Registry: Version-controlled catalog of trained models with metadata Drift Detection: Monitoring for statistical shift...

Firmware Testing Strategies: Hardware-in-the-Loop, Simulation, and CI/CD Pipelines | Embedded Systems Hub

Introduction Comprehensive firmware testing: unit testing with CMock/Unity, HIL with real hardware, instruction-set simulation (QEMU, Renode), and GitHub Actions/GitLab CI integration. This article provides a comprehensive technical deep-dive into the subject, covering theoretical foundations, practical implementation strategies, and real-world engineering trade-offs encountered in production embedded systems. Core Concepts Fundamental Principles Understanding the fundamental principles is essential before diving into implementation. This section covers the theoretical underpinnings that drive design decisions in embedded systems engineering. Key Terminology MCU/MPU: Microcontroller Unit / Microprocessor Unit - the compute engine RTOS: Real-Time Operating System - deterministic task scheduling HAL: Hardware Abstraction Layer - portable hardware interface BSP: Board Support Package - hardware-specific initialization OTA: Over-The-Air - remote firmware updates System Constraints Embedded...

Computer Vision for Robotics | Robotics Development Hub

Visual perception is the primary sensor modality for most autonomous robots. This guide covers end-to-end vision pipelines from camera calibration to high-level perception tasks, with practical ROS 2 integration. 1. Camera Models & Calibration 1.1 Pinhole Camera Model # Projection: u = fx * (X/Z) + cx, v = fy * (Y/Z) + cy # Intrinsic matrix K = [[fx, 0, cx], [0, fy, cy], [0, 0, 1]] # Distortion: radial (k1, k2, k3) + tangential (p1, p2) # OpenCV calibration import cv2 import numpy as np # Prepare object points (checkerboard corners in 3D) objp = np.zeros((6*9, 3), np.float32) objp[:, :2] = np.mgrid[0:9, 0:6].T.reshape(-1, 2) * square_size objpoints = [] # 3D points imgpoints = [] # 2D points for img_path in calibration_images: img = cv2.imread(img_path) gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY) ret, corners = cv2.findChessboardCorners(gray, (9, 6), None) if ret: corners2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), criteria) objpoin...

Robot Simulation with Gazebo & Ignition | Robotics Development Hub

Gazebo (now Ignition/Gazebo) is the standard for high-fidelity robot simulation. This guide covers SDFormat modeling, sensor plugins, physics configuration, ROS 2 integration, headless CI/CD, and domain randomization for sim-to-real transfer. 1. Gazebo Versions & Architecture Version Series ROS 2 Distro Status Gazebo 11 Classic Humble EOL Ignition Fortress Ignition Humble/Iron EOL Ignition Garden Ignition Iron/Jazzy Supported Gazebo Harmonic Gazebo (new) Jazzy/Kilted Current Gazebo Ionic Gazebo (new) Kilted/Rolling Latest 2. SDFormat Models 2.1 Model Structure false 0 0 0.1 0 0 0 5.0 0.01 0 0 0.01 0 0.02 0 0 0.05 0 0 0 0.4 0.3 0.2 0.4 0.3 0.2 0.7 0.7 0.7 1 0.7 0.7 0.7 1 base_link wheel_left -0.2 0.15 0 0 0 0 0 1 0 -1e16 1e16 10 20 0.1 0.01 0.5 0.001 0.001 0.0005 0.05 0.04 0.05 0.04 2.2 Nested Models & Includes model://my_robot_description robot_1 0 0 0 0 0 0 # gz sdf -p robot.urdf > robot.sdf 3. Sensor Plugins 3.1 Camera Sensor 0.2 0 0.1 0 0 0 1.047 640 480 R8G8B8 0.1 100 ga...

All Articles | Quantum Computing Hub

Complete implementations of Shor's factoring, Grover's search, VQE for ground state energy, and QAOA for combinatorial optimization with Qiskit and Cirq. Read Guide → Deep comparison of IBM Qiskit and Google Cirq: circuit construction, simulators, hardware access, transpilation, and migration strategies. Read Guide → Surface codes, stabilizer formalism, logical qubit encoding, syndrome extraction, and fault-tolerant logical gate implementations with practical Qiskit code. Read Guide → Quantum neural networks, variational quantum classifiers, quantum kernels, and hybrid quantum-classical training with PennyLane and Qiskit ML. Read Guide → MaxCut, TSP, portfolio optimization, and constraint satisfaction problems: QAOA circuit design, parameter optimization, and NISQ limitations. Read Guide → Categories Algorithms (1) Frameworks (1) Error Correction (1) QML (1) Optimization (1)