PADO-Pauli: A GPU-Accelerated Implementation of Pauli Propagation

Variational quantum algorithms utilize parameterized circuits many times during training, at new parameter values, over batches of data, and with gradients. Pauli propagation approximates the expectation values of such circuits classically by evolving the observable in the Heisenberg picture as a truncated sum of Pauli strings. We present PADO-Pauli, a GPU engine for Pauli propagation that compiles a circuit and its observables once into sparse matrices in which each rotation angle contributes only a cosine and a sine factor, so every later evaluation reuses the compiled program. It evaluates batches of parameters and data inputs embedded as rotation angles. By default its gradients come from a vector-Jacobian product registered with PyTorch's automatic differentiation, so they flow through the angles to any classical layer that produces them. PADO-Pauli also provides truncation by Pauli weight and coefficient size, and noise channels. Zero-filtering removes terms that do not contribute to an expectation value in the all-zero reference state and makes the batched forward pass about 1.5 times faster. Compared to cuPauliProp on an NVIDIA A100, PADO-Pauli evaluates up to 10 times faster on 4 to 12 qubits and uses up to 3.1 times less memory on 16 qubits. We check its accuracy against exact statevector simulation up to 28 qubits. These features make PADO-Pauli a practical toolkit for training variational quantum algorithms, including quantum machine learning models.