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.

#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 VQE, QAOA, and quantum machine learning. The classical-quantum split is where quantum advantage emerges: quantum for superposition/entanglement, classical for control and optimization.