Dynamiqs is a high-performance, differentiable quantum simulation library built on JAX. It solves the Schrödinger equation, Lindblad master equation, diffusive and jump stochastic master equations, and computes propagators and Floquet modes. The library is designed for GPU acceleration and scales to batched simulations over many Hamiltonians, initial states, or parameters. It provides machine-precision gradients via forward and reverse-mode automatic differentiation, making it suitable for quantum optimal control and parameter estimation. The architecture is modular: a hierarchy of integrators (adaptive ODE solvers via Diffrax, fixed-step Rouchon, matrix exponentiation, low-rank, and event-based) is coupled with custom array representations (dense and sparse diagonal DIA via DataArray subclasses). Time-dependent operators are supported through a hierarchy of TimeQArray classes. The library also includes plotting utilities, random state/operator generation, and extensive verification against analytical solutions. External dependencies include JAX, Diffrax, Equinox, and QuTiP (for compatibility). The codebase demonstrates strong engineering with a comprehensive test suite (including gradient and stochastic property tests), benchmark infrastructure, and CI/CD pipelines. It is used by the startup Alice & Bob for cat-qubit control and is under active development with a rapidly evolving API.