Title: ACCELERATING VARIATIONAL QUANTUM ALGORITHMS WITH MULTIPLE QUANTUM PROCESSORS. Abstract: Variational quantum algorithms (VQAs) are prime contenders that exploit near-term quantum machines to gain computational advantages over classical algorithms. As such, how to accelerate the optimization of modern VQAs has attracted great attention in past years. Here we propose a \texttt{QU}antum \texttt{DI}stributed \texttt{O}ptimization scheme (abbreviated as QUDIO) to address this issue. Conceptually, QUDIO utilizes a classical central server to partition the learning problem into multiple subproblems and allocate them to a set of quantum local nodes. In the training stage, all local nodes proceed with parallel training and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in the number of global iterations under the ideal scenario. Moreover, when the imperfection of the quantum system is considered, we prove that an increased synchronization time leads to a degraded convergence rate or even incurs divergent optimization. Numerical results on standard benchmarks illustrate that QUDIO can surprisingly reach a superlinear clock-time speedup in terms of the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with the quantum advantage. 