  With the progress in the quantum algorithm in recent years, much of the
existing literature claims the exponential quantum advantage against their
classical counterpart. However, many of these successes hinge on the assumption
that arbitrary states can be efficiently prepared in quantum circuits. In
reality, crafting a circuit to prepare a generic $n$-qubit quantum state
demands an operation count on the order of $\mathcal{O}(2^n)$, which is
prohibitively demanding for the quantum algorithm to demonstrate its advantage
against the classical one. To tackle this data-loading problem, numerous
strategies have been put forward. Nonetheless, most of these approaches only
consider a very simple and easy-to-implement circuit structure, which has been
shown to suffer from serious optimization issues.
  In this study, we harness quantum circuits as Born machines to generate
probability distributions. Drawing inspiration from methods used to investigate
electronic structures in quantum chemistry and condensed matter physics, we
present a novel algorithm "Adaptive Circuit Learning of Born Machine" (ACLBM)
that dynamically expands the ansatz circuit. Our algorithm is tailored to
selectively integrate two-qubit entangled gates that best capture the complex
entanglement present within the target state. Empirical results underscore the
proficiency of our approach in encoding real-world data through amplitude
embedding, demonstrating not only compliance with but also enhancement over the
performance benchmarks set by previous research.
