Quantum Chaos in Kicked Top
Quantum-classical correspondence is of fundamental interest as it allows for computing and analysing the quantum properties with respect to their classical counterparts. This helps us study the transition from the quantum to the classical. According to the correspondence principle, quantum mechanics should agree with classical mechanics in appropriate limits. In our first project, we show that currently available NISQ computers can be used for versatile quantum simulations of chaotic systems. We introduce a classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions. However, the connection between classical and quantum mechanics is not straightforward, especially in chaotic systems. The question of why a chaotic system, in certain situations, breaks the correspondence principle remains one of the open questions. Nevertheless, the breaking of Quantum classical correspondence for a large system i.e., the large value of j (but finite), is surprising. It suggests that the system never behaves classically in certain situations, irrespective of the system size. It is also worth exploring this strange behavior from an experimental point of view, as it will decide the parameters of the experimental setup designed for studying Quantum Chaos.
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