This paper presents "identification of purest quantum states," a novel method for identifying quantum systems least affected by noise, to address the quantum noise problem, a fundamental obstacle to the practical application of quantum technology. We present a rigorous paradigm for identifying the purest state among $K$ unknown $n$-qubit quantum states using a total of $N$ copies of the quantum states, and derive the first adaptive algorithm with an error probability $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$ for nondeterministic strategies. This fundamentally improves quantum property learning through measurement optimization. Furthermore, we develop a deterministic measurement protocol with an error bound $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, demonstrating a significant improvement over nondeterministic strategies, and quantitatively measure the performance of quantum memory and deterministic measurements. Finally, we establish a lower bound by showing that any strategy using a fixed-two-outcome nondeterministic POVM must suffer an error probability exceeding $\exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This work advances the characterization of quantum noise through an efficient learning framework and lays a theoretical foundation for quantum property learning that adapts to quantum noise, while providing a practical protocol for improving the reliability of quantum hardware.
