Classical training of quantum generative models based on Fermion Sampling

Quantum generative learning is a promising, "native" use-case for quantum computers, but it faces several trainability challenges. We show that these obstacles can be mitigated for certain restricted, structured quantum generative models through the possibility of efficient classical estimation of expectation values of local observables. These classical estimates enable fully classical training, removing the need for quantum gradient evaluations. Despite the classical efficiency of training, sampling from these circuits is widely believed to be classically intractable, suggesting a potential computational advantage. Thus, these models can be trained classically, whereas inference (sampling) has to be executed on a quantum device. We introduce Fermionic Born Machines as such classically trainable quantum generative models. The model uses parameterized magic states and fermionic linear optical (FLO) transformations with learnable parameters. Training exploits a decomposition of the magic states into Gaussian operators, which permits efficient estimation of expectation values. Via the Jordan–Wigner transformation, the FLO circuits can be implemented on qubit architectures to sample from the learned distribution during inference. Numerical experiments on systems exceeding 100 qubits demonstrate the performance of our model and training framework.