The computational hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP) directly determines Elliptic-Curve Cryptography (ECC) security. Quantum Annealing (QA) leverages its unique tunneling effects to effectively escape local optima. This paper proposes a quantum-annealing-based computational framework for attacking ECDLP by integrating QA with the index calculus method, achieving a quantum-solving attack on ECDLP. First, a relation-generation method based on Semaev summation polynomials is used to map the complex elliptic-curve point-addition constraints onto an Ising Hamiltonian. Next, by restructuring the penalty-term formulation and applying dynamic coefficient optimization, the parameter scale of the Ising Hamiltonian is compressed by 80%, thereby improving the QA success probability. Finally, the ECDLP is successfully modeled and solved on the D-Wave Advantage2 quantum computer. Experimental results demonstrate that the proposed quantum computing framework solves a 16-bit prime-field elliptic curve ECDLP on real quantum hardware, representing the highest experimental record publicly reported to date internationally, and further validating the practical attack potential and scalability of QA in cryptanalytic scenarios.