Transitions in Quantum Complexity

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A universal quantum simulator needs unlimited access to a so-called universal set of gates. Universal gates, however, are expensive and noisy and therefore a resource that must be used sparingly with current technology. Understanding how starting from economical designs one can achieve more universal quantum simulators with sparse resources is of fundamental importance in both the construction of realistic quantum computers and in the theoretical understanding of quantum complexity, quantum chaos, and even black hole physics. Advancing our understanding of quantum simulators and quantum computers is one of the main goals of the country's current endeavor in both fundamental and applied science. Being at the forefront of the upcoming quantum information industrial revolution will bring enormous benefits for the economy, in particular creating new opportunities for people from disadvantageous backgrounds and provide an impulse for the advancement of scientific education at all levels. How universal a quantum circuit is can be captured by how well it reproduces some average properties of quantum evolutions. In this project the group aims at studying how by doping circuits made of non-universal Clifford gates by means of non-Clifford gates one can drive transitions in quantum complexity and achieve a more universal coverage of the ensemble of quantum circuits. They study the transitions in quantum complexity by entanglement complexity, out-of-time-order correlation functions, unitary t-designs, and the behavior of such circuits under an entanglement cooling protocol. Moreover, they plan to apply techniques of machine learning by a deep neural network to both detect the transitions in quantum complexity and to optimize the circuit architecture given the density of non-Clifford gates.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.