Speaker
Description
Parameterized quantum circuits (PQCs) are increasingly studied as machine learning models, yet whether they can offer provable advantages over classical approaches remains largely open. In the context of generative modelling, Born Machines, which generate probability distributions according to the Born rule from parameterized quantum states, are a natural candidate for quantum advantage, as sampling is efficient on quantum hardware. Despite growing interest in Born Machines as generative models, rigorous learnability guarantees remain scarce.
In this work, we approach this problem through the lens of dequantization via classical surrogates. Exploiting the fact that Born Machines admit a tensor network representation as Matrix Product States (MPS), we focus on developing provably efficient algorithms for learning MPS distributions, thus yielding non-proper learning algorithms for Born Machines. We propose a spectral algorithm that recovers the MPS from $L$-th order marginals via a TT-SVD procedure. Under the condition that the $L$-th order marginals share the same rank structure as the underlying MPS, the algorithm achieves exact recovery with sample and computational complexity scaling linearly in the number of sites $N$ and polynomially in the bond dimension $r$. Our results identify sufficient conditions for the efficient learnability of Born Machines and contribute to the broader understanding of when quantum generative models can or cannot be efficiently dequantized.
| Topic | Tensor methods and quantum-inspired machine learning |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |