Random Circuits have emerged as an invaluable tool in the quantum mechanics’ toolkit. On one hand, the task of sampling outputs from a random circuit has established itself as a leading contender to experimentally demonstrate the intrinsic superiority of quantum computers using near-term, noisy platforms. On the other hand, random circuits have also been used to deduce far-reaching conclusions about the theoretical foundations of quantum information and communication. Furthermore, the dynamics of quantum objects undergoing random unitary evolution has been shown to display rich physics, enabling the use of tools of many-body physics to study quantum information. In the presence of measurements or monitoring, unitary dynamics compete with projective measurements to give rise to a phase transition in the creation of entanglement. Beyond entanglement, a phase transition has also been observed in a closely related measure called magic, which quantifies the "non-classicalness" of a quantum state. Finally, analytic insights from the study of random circuits can be used to deduce conclusions about error-correction and error-mitigation. In this dissertation talk, I discuss several ideas around the phase transitions in random circuits, and the analytic, numerical and experimental probes used to characterize them.
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