Seminar featuring Kazuki Ikeda, Osaka University
It is known that quantum phase transitions occur in the process of quantum annealing. The order of phase transition and computational efficiency are closely related with each other. Quantum computation starts with a non-entangled state and evolves into some entangled states, due to many body interactions and the dynamical delocalization of quantum information over an entire system's degrees of freedom (information scrambling). It is common to diagnose scrambling by observing the time evolution of single qubit Pauli operators with an out-of-timeorder correlator (OTOC). We aim at establishing a method to clarify those relations between phase transitions and scrambling by OTOCs. Using the p-spin model, we diagnose quantum phase transitions associated with quantum annealing and reverse annealing. In addition we provide a novel Majorana fermion model in which non-stoquastic dynamics of annealing can turn a first-order phase transition into a second-order phase transition. We also show that these phase transitions can be diagnosed by the OTOCs.