Stability and instability in quantum mechanics

Yakir Aharonov, Tomer Shushi

We show how the quantum hydrodynamical formulation of quantum mechanics converts the nonlocality in the standard wave-like description of quantum systems by an instability of the quantum system, which opens the door to a new way for studying quantum systems based on known methodologies for studying the stability of fluids. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.

É. Papp

Jincheng Zhang

Quantum-inspired feedback loops offer a novel approach to enhancing algorithm stability, particularly in dynamic environments. This paper explores the potential of incorporating quantum entanglement into a feedback mechanism designed to proactively detect and mitigate instability issues. We present a theoretical framework detailing the core principles, mechanisms, and expected outcomes of this approach. The goal is to develop a robust and adaptable strategy for improving the reliability of algorithms across a range of scenarios. This work provides a foundational investigation into the application of quantum mechanics to algorithm optimization, aiming for significant improvements in stability through a dynamically adjusted feedback system.

Emilio d’Emilio, Luigi E. Picasso

Giuliano Benenti, Giulio Casati

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.

Emilio d’Emilio, Luigi E. Picasso