Dynamics of the quantum search and quench-induced first-order phase transitions

Abstract

We investigate the excitation dynamics at a first-order quantum phase transition (QPT). More specifically, we consider the quench-induced QPT in the quantum search algorithm, which aims at finding out a marked element in an unstructured list. We begin by deriving the exact dynamics of the model, which is shown to obey a Riccati differential equation. Then, we discuss the probabilities of success by adopting either global or local adiabaticity strategies. Moreover, we determine the disturbance of the quantum criticality as a function of the system size. In particular, we show that the critical point exponentially converges to its thermodynamic limit even in a fast evolution regime, which is characterized by both entanglement QPT estimators and the Schmidt gap. The excitation pattern is manifested in terms of quantum domains walls separated by kinks. The kink density is then shown to follow an exponential scaling as a function of the evolution speed, which can be interpreted as a Kibble-Zurek mechanism for first-order QPTs.

9 pages, 7 figures

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• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Dynamics of a Nonequilibrium Discontinuous Quantum Phase Transition in a Spinor Bose-Einstein Condensate
• Dynamics of Entanglement and the Schmidt Gap in a Driven Light-Matter System
• Observation of heat scaling across a first-order quantum phase transition in a spinor condensate
• Quantum steering ellipsoids and quantum obesity in critical systems