Reliable Analog Quantum Simulation and Quantum Complexity

An analog quantum simulator does not employ digital gates with quantum error correction. Yet, one hopes such devices can achieve a “quantum advantage,” i.e., enable the simulation of some property that cannot be simulated efficiently on a classical computer. Typically, one considers “universal” properties in condensed matter, as these are the quantities that are robust in the presence of perturbations [1]. What is the relationship between robustness and complexity? Are the robust properties efficiently simulatable on a classical computer, and the complex properties hyper-sensitive to perturbation? To address these questions, we seek to quantify the reliability of an analog quantum simulator while simulating complex systems and thereby identify these universal quantities. We study a “programmable” analog quantum simulator in the 16-dimensional Hilbert space based on optimal control of atomic spins in cesium [2], and study the basic paradigms such as the excited state quantum phase transitions [3] in the Lipkin-Meshkov-Glick (LMG) model [3].

References:
[1] J. Preskill, ArXiv eprints (2018) arXiv: 1801. 00862
[2] Anderson, B. E., et al. , Phys. Rev. Lett. 114.24 : 240401(2015).
[3] Santos, Lea F., et al. , Phys. Rev. A 94.1 : 012113(2016).