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With the progress in the quantum algorithm in recent years, much of theexisting literature claims the exponential quantum advantage against theirclassical counterpart. However, many of these successes hinge on the assumptionthat arbitrary states can be efficiently prepared in quantum circuits. Inreality, crafting a circuit to prepare a generic $n$-qubit quantum statedemands an operation count on the order of $\mathcal{O}(2^n)$, which isprohibitively demanding for the quantum algorithm to demonstrate its advantageagainst the classical one. To tackle this data-loading problem, numerousstrategies have been put forward. Nonetheless, most of these approaches onlyconsider a very simple and easy-to-implement circuit structure, which has beenshown to suffer from serious optimization issues.  In this study, we harness quantum circuits as Born machines to generateprobability distributions. Drawing inspiration from methods used to investigateelectronic structures in quantum chemistry and condensed matter physics, wepresent a novel algorithm "Adaptive Circuit Learning of Born Machine" (ACLBM)that dynamically expands the ansatz circuit. Our algorithm is tailored toselectively integrate two-qubit entangled gates that best capture the complexentanglement present within the target state. Empirical results underscore theproficiency of our approach in encoding real-world data through amplitudeembedding, demonstrating not only compliance with but also enhancement over theperformance benchmarks set by previous research.

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Data Loading