Quantum Dynamical Complexity and Reliability of Analog Quantum Simulation*

The NISQ era is characterized by the absence of fully fault-tolerant quantum simulators, which raises a question about the reliability of such devices. To address this, we seek to quantify the reliability of an analog quantum simulator, which doesn’t have access to error correction, in the presence of perturbations that make the dynamics quantum chaotic. In doing so we seek to identify the relationship between the robustness of the quantities that we seek to extract from the simulator and the dynamical complexity of the analog evolution. As one measure, we quantify the complexity by the number of variables that one must track to approximately yield the output within a desired accuracy. We address these questions by studying the basic paradigms such as the ground state and the excited state quantum phase transitions in the Lipkin-Meshkov-Glick (LMG) model[1].

References:
[1]Marco Távora, and Francisco Pérez-Bernal. "Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation." Physical Review A 94.1 (2016): 012113