Observation of a Dynamical Quantum Phase Transition by a Superconducting Qubit Simulation

A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum-state return amplitude, analogous to nonanalyticity of the free-energy density at the critical temperature in macroscopic systems. A variety of many-body systems can be represented in momentum space as a spin-1/2 state evolving on the Bloch sphere, where each momentum mode is decoupled and thus can be simulated independently by a single qubit. Here, we report the observation of a dynamical quantum phase transition in a superconducting qubit simulation of the quantum-quench dynamics of many-body systems. We take the Ising model with a transverse field as an example for demonstration. In our experiment, the spin state, which is initially polarized longitudinally, evolves based on a Hamiltonian with adjustable parameters depending on the momentum and strength of the transverse magnetic field. The time-evolving quantum state is read out by state tomography. Evidence of dynamical quantum phase transitions, such as paths of time-evolution states on the Bloch sphere, nonanalytic behavior of the dynamical free energy, and the emergence of Skyrmion lattice in momentum-time space, is observed. The experimental data agrees well with theoretical and numerical calculations. The experiment demonstrates explicitly the topological invariant, both topologically trivial and nontrivial, for dynamical quantum phase transitions. Our results show that the quantum phase transitions of this class of many-body system can be simulated successfully with a single qubit by varying certain control parameters over the corresponding momentum range.