What is a quantum-inspired evolutionary algorithm (QEA) in C and how is it implemented?

Table of Contents

• Introduction to QEA
• Implementation of QEA in C
  • Steps to Implement QEA
  • C Code for QEA
• Explanation of the Code
  • 1. Representation of Quantum Bits
  • 2. Measurement Process
  • 3. Fitness Evaluation
  • 4. Quantum Rotation Update
  • 5. Iteration Until Convergence
• Advantages of QEA
• Applications of QEA
• Conclusion

Introduction to QEA

A Quantum-Inspired Evolutionary Algorithm (QEA) is an optimization technique that takes inspiration from quantum computing principles while utilizing classical evolutionary algorithms. It incorporates quantum bits (Q-bits) and superposition principles to improve search space exploration and convergence speed.

QEA is useful in solving combinatorial optimization problems, such as traveling salesman problem (TSP), knapsack problem, and job scheduling problems.

Implementation of QEA in C

Here’s a basic implementation of a Quantum-Inspired Evolutionary Algorithm (QEA) in C to solve an optimization problem.

Steps to Implement QEA

1. Initialize Quantum Bit Population: Represent the population using quantum bits.
2. Quantum Rotation Update: Adjust Q-bit values using rotation gates.
3. Observation: Convert quantum representation into classical solutions.
4. Evaluation: Compute the fitness of each individual.
5. Selection & Update: Choose the best individuals and update Q-bit angles.
6. Repeat Until Convergence: Iterate until the stopping condition is met.

C Code for QEA

Explanation of the Code

1. Representation of Quantum Bits

• Each quantum bit is represented by an angle θ.
• The probability of obtaining 0 or 1 is determined using the sine function.

2. Measurement Process

• The quantum state collapses into a classical binary value (0 or 1) based on probability.

3. Fitness Evaluation

• A simple fitness function is used (maximizing the number of 1s).

4. Quantum Rotation Update

• The algorithm updates quantum angles to guide the population toward better solutions.

5. Iteration Until Convergence

• The best solution is selected in each iteration, and quantum bits are updated accordingly.
• The algorithm stops if an optimal solution is found.

Advantages of QEA

• Fast Convergence: QEA explores the search space efficiently due to quantum principles.
• Better Exploration and Exploitation: Uses superposition and probabilistic updates.
• Effective for Combinatorial Optimization Problems.

Applications of QEA

• Job Scheduling Problems
• Traveling Salesman Problem (TSP)
• Knapsack Optimization
• Neural Network Training
• Financial Forecasting

Conclusion

Quantum-Inspired Evolutionary Algorithm (QEA) is a powerful optimization method that mimics quantum principles while being executed on classical hardware. The above C implementation demonstrates how QEA can be used for binary optimization problems, making it useful for various AI and computational optimization tasks.