We apply a new hardware and software platform called the Hamiltonian Engine for Radiotherapy Optimization (HERO) to the problem of Intensity-Modulated Radiation Therapy (IMRT) treatment planning. HERO solves large general-form binary optimization problems by decomposing them into sub-problems and approximating them using a quadratic pseudo-boolean function. Optimizing the resulting function becomes a quadratic unconstrained binary optimization (QUBO) problem, which has been widely studied and has numerous applications in various fields. A Quantum Annealer (QA) approach has been previously investigated to solve QUBO problems, including IMRT optimization. However, the QA can only accommodate a small number of variables and requires several hours to obtain optimized plans. HERO acts as an optimizer for QUBO problems, which not only addresses these shortcomings but also relies solely on conventional hardware design while operating at room temperature. We evaluate HERO on seven prostate IMRT cases with clinical objectives, each using approximately 6000 beamlets. Our method was compared to the commercial treatment planning software, Eclipse, for both time-to-solution and plan quality. HERO solves most cases in about 30 seconds, with significantly lower objective function scores than Eclipse. The results indicate that HERO is promising for radiation therapy optimization problems. Additionally, HERO has the potential to be applied to Volumetric-Modulated Arc Therapy (VMAT) and other complex types of treatment planning.