Speaker
Description
Pauli propagation is a powerful framework for simulating quantum systems by tracking the evolution of Pauli operators, yet its scope has so far been limited to estimating expectation values. We extend it to sampling from quantum states, introducing an algorithm that draws bitstrings directly from truncated Pauli expansions. While the very truncation that makes Pauli propagation efficient renders the represented operator non-positive-semidefinite - so that its Born ''probabilities'' can be negative and standard sampling is ill-defined - we resolve this with a locally normalized conditional sampling procedure that builds a valid distribution on the fly, bypassing the intractable global renormalization over all $2^n$ bitstrings. We prove that the total variation distance to the true Born distribution scales linearly with the truncation error, and that the cost per sample is linear in the number of retained Pauli terms. We deploy the sampler on thermal states prepared by imaginary-time Pauli propagation - a natural setting, since the evolution starts from the identity, the sparsest Pauli operator. Because quantum Boltzmann machines (QBMs) are parameterized thermal states, this combination further enables their training for generative learning tasks; numerically, we demonstrate both accurate sampling from truncated thermal states and successful training of these models. More broadly, our method offers a new pathway for simulating, sampling from, and training models of complex quantum systems on classical hardware.
| Topic | Tensor methods and quantum-inspired machine learning |
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