Quantum technology is the next frontier in the information revolution that powers the nation's economic engine. Machines that process information using the microscopic laws of quantum physics can solve critical problems that are intractable with even the most powerful supercomputers, such as design of new high tech materials and pharmaceuticals. A general purpose quantum computer is still years in the future, but current quantum technology is now sufficiently advanced for private companies and government agencies to pursue the development of special purpose "quantum simulators" that can be applied to select problems. Unfortunately, the operation of such machines can be very sensitive to noise and imperfection, in a manner closely analogous to the "butterfly effect" whereby even the smallest disturbance (metaphorically, the flap of a butterfly's wing) can affect the predictive power of weather forecasts. This project seeks to better understand the tradeoff between a quantum simulator's power to solve hard computational problems, and the extreme fragility of its predictions when subject to noise and imperfections. Such understanding will be essential for the successful application of quantum technology to problems in science and engineering. Quantum simulation requires access to highly entangled many body systems whose dynamics are complex. It has long been a concern that such systems exhibit "quantum chaos" which will make any large scale quantum simulation hypersensitive to imperfections. Yet, at the same time it is argued that requirements for a special purpose quantum simulation are less stringent than for universal digital quantum computing. This, then, is the tension at the heart of quantum simulation: Can one have the complex dynamics needed to access massively entangled states, and at the same time have a reliable device that is not rendered inoperable by hypersensitivity? In short: Can one trust the output of a non-trivial quantum simulator? The proposed research will put those questions to the test in experiments with a quantum simulator based on the spins of individual cesium atoms. This test bed provides access to state-of-the-art control and diagnostics, and offers the ability to drive and observe a nearly unlimited variety of complex dynamics, including many of the paradigmatic models of analog quantum simulation currently explored elsewhere. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.