Quantum simulation using noisy unitary circuits and measurements

Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steady-state entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.