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The quantum matter synthesizer (QMS) is a new quantum simulation platform in which individual particles in a lattice can be resolved and re-arranged into arbitrary patterns. The ability to spatially manipulate ultracold atoms and control their tunneling and interactions at the single-particle level allows full control of a many-body quantum system. We present the design and characterization of the QMS, which integrates into a single ultra-stable apparatus a two-dimensional optical lattice, a moving optical tweezer array formed by a digital micromirror device, and site-resolved atomic imaging. We demonstrate excellent mechanical stability between the lattice and tweezer array with relative fluctuations below 10 nm, diffraction-limited imaging at a resolution of 655 nm, and high-speed real-time control of the tweezer array at a 2.52 kHz refresh rate, which will be adopted to realize fast rearrangement of atoms. The QMS also features new technologies and schemes, such as nanotextured anti-reflective windows and all-optical long-distance transport of atoms. [ABSTRACT FROM AUTHOR]