CUDA-Q is NVIDIA's open-source C++/Python framework for hybrid quantum-classical computing. Targets variational algorithms (VQE, QAOA) with GPU-accelerated classical optimization and quantum simulation. Supports multiple backends (GPU simulators, vendor hardware). Includes automatic differentiation for gradients. Designed for HPC workflows and large-scale simulation.

The following example demonstrates a variational quantum eigensolver (VQE) for a two-qubit system:

import cudaq
from scipy.optimize import minimize
 
# Define ansatz for VQE
def ansatz(theta):
    qvec = cudaq.qvector(2)
    cudaq.h(qvec[0])
    cudaq.ry(theta[0], qvec[0])
    cudaq.cx(qvec[0], qvec[1])
    return cudaq.observe(qvec, cudaq.pauli_word({0: 'Z', 1: 'Z'}))
 
# Minimize ⟨ZZ⟩ with COBYLA
result = minimize(lambda θ: ansatz(θ).expectation(), x0=[0.0], method='COBYLA')
print(f"Ground state energy: {result.fun:.4f}")