  Leveraging the extraordinary phenomena of quantum superposition and quantum
correlation, quantum computing offers unprecedented potential for addressing
challenges beyond the reach of classical computers. This paper tackles two
pivotal challenges in the realm of quantum computing: firstly, the development
of an effective encoding protocol for translating classical data into quantum
states, a critical step for any quantum computation. Different encoding
strategies can significantly influence quantum computer performance. Secondly,
we address the need to counteract the inevitable noise that can hinder quantum
acceleration. Our primary contribution is the introduction of a novel
variational data encoding method, grounded in quantum regression algorithm
models. By adapting the learning concept from machine learning, we render data
encoding a learnable process. Through numerical simulations of various
regression tasks, we demonstrate the efficacy of our variational data encoding,
particularly post-learning from instructional data. Moreover, we delve into the
role of quantum correlation in enhancing task performance, especially in noisy
environments. Our findings underscore the critical role of quantum correlation
in not only bolstering performance but also in mitigating noise interference,
thus advancing the frontier of quantum computing.
