Quantum chaos for real

W. D. Heiss

J. A. Louw, W.‐H. Steeb

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Jincheng Zhang

Quantum Chaos Field Theory (QCFT) offers a novel computational framework for optimization problems, leveraging the dynamic properties of quantum chaos. This paper explores the design and implementation of a real-space optimization algorithm based on QCFT, demonstrating its potential for efficient solution of complex problems and the generation of high-quality results. The core mechanism centers around the dynamic mapping of optimization landscapes and the application of quantum entanglement and superposition to enhance search efficiency. We present a preliminary implementation demonstrating the algorithm's effectiveness in solving a set of challenging optimization scenarios, highlighting the advantages of QCFT over traditional methods.

A. V. Poshakinskiy, Janet Zhong, Alexander N. Poddubny

We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave function in real space. This indicates the Bethe ansatz breakdown and the onset of quantum chaos, in stark contrast to the conventional integrable problem of two interacting bosons in a box. We identify the long-range waveguide-mediated coupling between the atoms as the key ingredient of chaos and nonintegrability. Our results provide new insights in the interplay between order, chaos, and localization in many-body quantum systems and can be tested in state-of-the-art setups of waveguide quantum electrodynamics.

Tara Bahadur Rana, Yadav Raj Dahal, Kiran Adhikari

In this work, we study pseudo entropy and spectral dynamics in quantum spin chains (Heisenberg XXZ model and the mixed-field Ising model) to investigate whether they can serve as diagnostics of quantum chaos. First, we derive an exact relation between the real part of the thermal pseudo entropy and the spectral form factor. This provided evidence that pseudo entropy could exhibit the characteristic dip, logarithmic ramp, and plateau, implying the precise manner in which pseudo entropy probes chaos. We found that the imaginary part, while it does not diagnose chaos, can still provide crucial information about Fisher zeros that is not available in the real counterpart. For spatial pseudo entropy in the XXZ chain, we find that the logarithmic critical scaling persists in both integrable and chaotic regimes, and that the non-positivity conjecture holds. Finally, we derive an exact connection between pseudo entropy, relative pseudo entropy, and spectral complexity with a potential connection to holography.