QuantumSim is a lightweight and extensible C++ library designed to simulate and visualize the behavior of single-qubit quantum systems. It provides a modular, object-oriented framework to represent qubits, apply quantum gates, and visualize gate sequences as readable circuit diagrams in the command line.

The project is built with mathematical correctness and extensibility in mind — serving both as a learning tool and as a foundation for larger quantum simulation frameworks.

• Models a single qubit state as: [ |\psi⟩ = \alpha|0⟩ + \beta|1⟩ ] with the normalization condition ( |\alpha|^2 + |\beta|^2 = 1 ).
• Supports complex-valued amplitudes (std::complex<double>).
• Performs automatic normalization check on creation and after every gate operation.

• Implements a polymorphic base class Gate defining the common interface for all quantum gates.
• Derived gate classes (Hadamard, Pauli-X, Pauli-Y, Pauli-Z) initialize their respective 2×2 unitary matrices.
• Each gate performs standard matrix–vector multiplication on the qubit state.

Each gate enforces proper dimensionality and throws exceptions on invalid application.

QuantumSim allows you to manipulate qubit states by applying quantum gates directly through the applyGate() method.

#include "Hadamard.h"
#include "XGate.h"
#include "ZGate.h"
#include "Qbit.h"
#include <iostream>
using namespace std;

int main() {
    Hadamard H;
    XGate X;
    ZGate Z;

    Qbit q({1,0}, {0,0}); // Initialize |0⟩

    cout << "Initial: " << q << endl;

    q.applyGate(H);  // Create superposition
    q.applyGate(X);  // Flip amplitudes
    q.applyGate(Z);  // Apply phase flip

    cout << "Final: " << q << endl;
    q.printCircuit();  // Visualize applied sequence
}