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

Table of Contents

• Introduction
• How QEA Works
  • 1. Quantum Representation
  • 2. Quantum Population Initialization
  • 3. Rotation Gate Update
  • 4. Measurement
  • 5. Fitness Evaluation and Selection
• Implementation of Quantum-Inspired Evolutionary Algorithm (QEA) in C++
  • C++ Code Example:
• Key Steps in the Example
  • 1. Initialization
  • 2. Measurement
  • 3. Rotation Gate Update
  • 4. Iteration
• Conclusion

Introduction

A Quantum-Inspired Evolutionary Algorithm (QEA) is an evolutionary computation technique that leverages principles from quantum computing, such as quantum superposition and probabilistic representation, to solve optimization problems. It does not involve actual quantum computing hardware but mimics quantum properties to enhance evolutionary algorithms' performance.

QEA uses quantum bits (qubits) to represent multiple potential solutions simultaneously, which provides the algorithm with better exploration capabilities in the search space compared to classical evolutionary algorithms.

How QEA Works

1. Quantum Representation

Instead of using traditional binary or real-valued representation, QEA uses qubits for encoding solutions. A qubit is represented by a probability amplitude, which enables a solution to exist in multiple states simultaneously.

2. Quantum Population Initialization

The algorithm starts by initializing a population of individuals. Each individual is represented by a quantum bit (qubit) state, defined by two parameters, α\alphaα and β\betaβ, which represent the probability amplitudes of 0 and 1.

3. Rotation Gate Update

At each iteration, QEA applies quantum gates (rotation gates) to update the qubit states based on the fitness of the solutions. This operation enables the algorithm to explore new solutions based on the best ones.

4. Measurement

After updating the qubit states, the quantum states are measured to extract classical binary solutions that represent the actual solutions to the optimization problem. These are then evaluated using the fitness function.

5. Fitness Evaluation and Selection

The fitness of each measured solution is evaluated, and the best solutions are selected for the next generation. The process continues until a stopping criterion is met.

Implementation of Quantum-Inspired Evolutionary Algorithm (QEA) in C++

Here is an example of how to implement the Quantum-Inspired Evolutionary Algorithm (QEA) in C++:

C++ Code Example:

Key Steps in the Example

1. Initialization

The population is initialized with individuals having their qubits in a superposition state where each qubit has equal probability of being 0 or 1.

2. Measurement

Each individual’s qubits are measured to generate classical binary solutions, which are evaluated using the fitness function (in this case, a sphere function).

3. Rotation Gate Update

The rotation gate is applied to update qubit states. The qubits rotate toward the best solution found so far, gradually refining the population toward better solutions.

4. Iteration

The process iterates over multiple generations, updating the population and improving the fitness of the solutions.

Conclusion

The Quantum-Inspired Evolutionary Algorithm (QEA) applies quantum concepts like superposition and rotation gates to enhance the performance of classical evolutionary algorithms. In this C++ implementation, QEA is demonstrated with an objective function and classical binary optimization. Its ability to explore and exploit solutions makes it highly suitable for complex optimization tasks.