Search for: All records

Abstract Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum-inspired generative models, such as Born machines based on the matrix product state (MPS) framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator-valued measurements (POVMs), replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model’s expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces negative log-likelihood compared to one-hot embeddings, with higher physical dimensions further enhancing single-site probabilities and multi-site correlations. The model also outperforms GPT-2 in single-site estimation and achieves competitive correlation modeling, showcasing the potential of trainable POVM embeddings for complex data correlations in quantum-inspired sequence modeling. 

We present a formulation for investigating quench dynamics acrossquantum phase transitions in the presence of decoherence. We formulatedecoherent dynamics induced by continuous quantum non-demolitionmeasurements of the instantaneous Hamiltonian. We generalize thewell-studied universal Kibble-Zurek behavior for linear temporal driveacross the critical point. We identify a strong decoherence regimewherein the decoherence time is shorter than the standard correlationtime, which varies as the inverse gap above the groundstate. In thisregime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})} t - ∼ τ 2 ν z / ( 1 + 2 ν z ) for when the system falls out of equilibrium and the associatedfreeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})} ξ ‾ ∼ τ ν / ( 1 + 2 ν z ) show power-law scaling with respect to the quench rate 1/\tau 1 / τ ,where the exponents depend on the correlation length exponent \nu ν and the dynamical exponent z z associated with the transition. The universal exponents differ fromthose of standard Kibble-Zurek scaling. We explicitly demonstrate thisscaling behavior in the instance of a topological transition in a Cherninsulator system. We show that the freeze-out time scale can be probedfrom the relaxation of the Hall conductivity. Furthermore, onintroducing disorder to break translational invariance, we demonstratehow quenching results in regions of imbalanced excitation densitycharacterized by an emergent length scale which also shows universalscaling. We perform numerical simulations to confirm our analyticalpredictions and corroborate the scaling arguments that we postulate asuniversal to a host of systems.