July 8, 2024 | Xhek Turkeshi, Emanuele Tirrito, Piotr Sierant
The paper investigates the dynamics of magic resources in random quantum circuits, focusing on the Calderbank-Shor-Steane (CSS) entropy as a scalable measure of non-stabilizerness. The authors explore how magic resources are generated and spread in systems of qudits under generic, non-integrable, local unitary dynamics. They introduce the CSS entropy, which generalizes the stabilizer Rényi entropy and captures the non-stabilizerness of many-body systems. By combining the replica trick and Haar average methods, they express the circuit-averaged CSS entropy as a tensor network contraction, enabling the study of systems up to $N = 1024$ qudits. The main finding is that the long-time saturation value of the CSS entropy is reached at times proportional to $\log(N)$, scaling logarithmically with the system size. This behavior is contrasted with the ballistic growth of entanglement entropy, which scales linearly with the system size. The authors conjecture that these findings describe the phenomenology of non-stabilizerness growth in a broad class of chaotic many-body systems.The paper investigates the dynamics of magic resources in random quantum circuits, focusing on the Calderbank-Shor-Steane (CSS) entropy as a scalable measure of non-stabilizerness. The authors explore how magic resources are generated and spread in systems of qudits under generic, non-integrable, local unitary dynamics. They introduce the CSS entropy, which generalizes the stabilizer Rényi entropy and captures the non-stabilizerness of many-body systems. By combining the replica trick and Haar average methods, they express the circuit-averaged CSS entropy as a tensor network contraction, enabling the study of systems up to $N = 1024$ qudits. The main finding is that the long-time saturation value of the CSS entropy is reached at times proportional to $\log(N)$, scaling logarithmically with the system size. This behavior is contrasted with the ballistic growth of entanglement entropy, which scales linearly with the system size. The authors conjecture that these findings describe the phenomenology of non-stabilizerness growth in a broad class of chaotic many-body systems.