# Hybrid Quantum-Classical Computing

**Hybrid quantum-classical computing** interleaves quantum operations with classical computation. Classical code drives quantum kernels, processes results, and makes decisions—all in the same program. This is essential for variational algorithms, error mitigation, and real-time feedback.

CUDA-Q's native C++ support makes hybrid programming natural: quantum kernels are C++ functions, results flow back to classical code seamlessly.

```cpp
#include "cudaq.h"
#include <vector>
#include <cmath>

// Quantum kernel: measure qubit state
struct MeasureState {
  void operator()(double angle) __qpu__ {
    cudaq::qvector q(1);
    ry(angle, q[0]);
    mz(q[0]);
  }
};

// Classical optimization loop
int main() {
  std::vector<double> angles;
  double best_cost = 1e9;
  
  // Classical loop driving quantum kernel
  for (double angle = 0.0; angle < M_PI; angle += 0.1) {
    // Execute quantum kernel with parameter
    auto result = cudaq::sample<MeasureState>(1000, angle);
    
    // Process classical result
    double cost = result.probability("1");  // P(|1⟩)
    
    if (cost < best_cost) {
      best_cost = cost;
      angles.push_back(angle);
    }
  }
  
  printf("Best angle: %.3f, Best cost: %.6f\n", angles.back(), best_cost);
  return 0;
}
```

Hybrid computing enables [[cuda-q-vqe|VQE]], [[cuda-q-qaoa|QAOA]], and quantum machine learning. The classical-quantum split is where quantum advantage emerges: quantum for superposition/entanglement, classical for control and optimization.