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Soon after Shor's algorithm and the explosion of quantum information science, Serge Haroche and JeanMichel Raimond asked in a famous 1996 Physics Today Article, "Quantum Computing: Dream or Nightmare?". They weren't alone. In the early days some of the pioneers, like Ralf Landauer and Bill Unruh, rightfully questioned whether the exponential reduction in computational complexity would be offset by the exponential sensitivity to noise and decoherence. In 1996 quantum error correction had just been "discovered" but faulttolerance was not yet fully established. Without faulttolerant quantum error correction, everyone understood that true computational advantage in implementing quantum algorithms, like Shor's, was not possible. In the intervening years, quantum simulation of matter was seen as lower hanging fruit, with much less demanding requirements for precision control and isolation from the environment. This is because phases are matter are "macrostates" rather than "microstates"and by definition, robust to the exact configuration of the constituents. In contrast, for Shor's algorithm, the bitflip on any single qubit can be completely catastrophic. It then behooves us to ask, if the macrostate is robust to imperfections, might it be computationally simple? By contrast, we expect the most nonclassical quantum complex states to be hypersensitive to decoherence, as Wojciech Zurek taught us in understanding the quantumtoclassical transition. In this seminar I will revisit these questions, exploring the tradeoff between robustness and complexity and the road to achieving quantum computational complexity in the modern NISQera. Short Bio: Ivan Deutsch is Distinguished Professor & Regents' Professor of Physics & Astronomy at the University of New Mexico, and Director of the Center for Quantum Information and Control (CQuIC). He works at the interface of AMO physics, quantum optics, and quantum information theory in both implementations of quantum information processors and their foundational properties. He did his bachelors at MIT and received his PhD from UC Berkeley, joining the faculty at UNM in 1995, where together with Carl Caves, he established the Quantum Information Science group. He leads Quantum New Mexico (QNM), the program to solidify New Mexico as a Quantum Information Science hub for the nation, in a collaboration between UNM, Sandia National Labs, Los Alamos National Labs, and other institutions across the state. Host: Samuel Slezak (CCS3) 