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Updated: Jul 9, 2025
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
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Instantons and the quantum bound to chaos
Vijay Ganesh Sadhasivam1, Lars Meuser1,2, David R Reichman3
1Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.
Summary
Quantum thermal fluctuations and barrier instantons are key to understanding the quantum chaos bound. This study reveals their crucial role in information scrambling rates within quantum systems.
Area of Science:
- Quantum Information Theory
- Statistical Mechanics
- Quantum Chaos
Background:
- Information scrambling in quantum systems is quantified by out-of-time-ordered correlators.
- The Lyapunov exponent, measuring scrambling rate, is predicted to obey a universal bound.
- Previous work suggested a quantum-statistical origin for this bound.
Purpose of the Study:
- To elucidate the quantum-statistical origins of the universal bound on information scrambling.
- To demonstrate the necessity of quantum thermal fluctuations for reproducing the bound.
- To establish a link between instanton stability and the quantum chaos bound.
Main Methods:
- Utilizing path-integral techniques to model quantum dynamics.
- Incorporating quantum thermal fluctuations (tunneling, zero-point energy) into classical dynamics.
- Propagating quantum-Boltzmann-conserving classical dynamics for a system with a potential barrier.
Main Results:
- A minimal theory reproducing the bound requires contributions from quantum thermal fluctuations.
- The bound is governed by the stability of thermal fluctuations around barrier instantons.
- Instanton formation and stability are intrinsically linked to the quantum chaos bound.
Conclusions:
- Quantum thermal fluctuations are essential for imposing the universal bound on quantum information scrambling.
- The stability of instanton-dominated thermal fluctuations dictates the scrambling rate bound.
- A fundamental connection exists between delocalized structures like instantons and the quantum chaos bound.
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