As physical realizations of quantum computers move closer towards practical applications, the need for tools to analyze and verify quantum algorithms grows. Among the algorithms and data structures used to tackle such problems, decision diagrams (DDs) have shown much success. However, an obstacle with DDs is their efficient parallelization, and while parallel speedups have been obtained for DDs used in classical applications, attempts to parallelize operations for quantum-specific DDs have yielded only limited success. In this work, we present an efficient implementation of parallel edge-valued DDs, which makes use of fine-grained task parallelism and lock-free hash tables. Additionally, we use these DDs to implement two use cases: simulation and equivalence checking of quantum circuits. In our empirical evaluation we find that our tool, Q-Sylvan, shows a single-core performance that is competitive with the state-of-the-art quantum DD tool MQT DDSIM on large instances, and moreover achieves parallel speedups of up to x18 on 64 cores.