Building quantum resources via shallow circuits

Present-day programmable quantum processors can reliably implement only circuits of limited depth because of noise and experimental imperfections. This limitation raises the question of how much many-body quantum complexity can be generated using a small number of sequential operations. The question is particularly relevant to quantum state preparation, where one seeks to prepare states using circuits that are as shallow as possible. In this context, shallow circuits provide a practically motivated setting in which to study the generation of quantum many-body complexity. One way of characterizing such complexity is through quantum resource theories. Indeed, different physical and operational settings identify certain states and operations as freely available, while those lying outside these restricted sets constitute resources. Quantum resource theories provide a systematic framework for characterizing and quantifying such resources. In this thesis, we focus on the entanglement, non-stabilizerness, and fermionic non-Gaussianity resources and investigate how rapidly they can be generated by local quantum dynamics, focusing on one-dimensional brickwork circuits. The main novel contributions of this work are the calculation of how non-stabilizerness and fermionic non-Gaussianity grow in Haar-random brickwork circuits, together with the determination of the maximal fermionic non-Gaussianity achievable in brickwork circuits. The results show that shallow local dynamics can rapidly generate substantial quantum resources.