Quantum chaos as a lens into system performance

Complex quantum devices in the noisy, intermediate scale regime have unique challenges in testing: how do we understand their performance when we are unable to classically simulate their behavior, but their noise levels are too high for many fault-tolerance-focused metrology approaches to apply? Fortunately, we can take advantage of two different elements: first, the existence of exact solutions to larger quantum systems, which comes in direct analogy to the existence of integrable systems in classical dynamics. The second is the robustness of classical integrable models to small perturbations, leading to ‘islands of stability’ and regions of predictable behavior even with small amounts of noise.

Analogous to classical mechanics, quantum trajectories can trace out stable, perturbation-resistant orbits in the phase space, or they can wander into the unpredictable chaotic regime, eventually erasing all memory of the initial position. We look for the pockets—or islands—in the phase space of near-integrable quantum systems where the trajectories are stable against small perturbations. These so-called islands of stability are especially valuable for quantum technologies, which often rely on precisely controlling the dynamics of microscopic particles, and may enable testing and performance characterization of complex quantum systems. Understanding the mechanism behind the formation of these islands could therefore provide a path to building better quantum devices. 

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