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Published on: June 8, 2018
Universal energy-space localization and stable quantum phases against time-dependent perturbations
Hongye Yu1,2, Tzu-Chieh Wei3,4
1C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, New York, NY, USA. hongye.yu@stonybrook.edu.
Nature Communications
|July 14, 2026
Summary
Quantum systems can maintain stability against time-dependent perturbations through energy-space localization. This phenomenon protects quantum states and impacts quantum algorithms, especially for optimization problems.
Area of Science:
- Quantum Many-Body Physics
- Quantum Information Science
- Non-Equilibrium Dynamics
Background:
- Stability is crucial for quantum many-body phases, but rigorous analysis typically focuses on static perturbations.
- The stability of quantum systems against generic time-dependent perturbations remains a significant open question.
Purpose of the Study:
- To identify and prove a universal phenomenon of stability against time-dependent perturbations in quantum systems.
- To explore the implications of this stability for quantum error correction codes and optimization algorithms.
Main Methods:
- Investigated the dynamics of quantum states under time-dependent q-local Hamiltonians.
- Proved the phenomenon of exponential energy-space localization and its robustness under perturbations.
- Applied the findings to analyze the stability of classical and quantum Low-Density Parity-Check (LDPC) codes.
Main Results:
- Identified a universal phenomenon where quantum states exponentially localize in an energy window under time-dependent perturbations.
- Demonstrated that this energy-space localization is stable against generic time-dependent perturbations.
- Showed that LDPC codes remain localized near their original codewords for exponentially long times.
- Revealed that this stability can hinder quantum Hamiltonian-based algorithms for optimization problems with clustered solutions.
Conclusions:
- The discovered energy-space localization provides a new mechanism for quantum system stability under dynamic perturbations.
- This work offers novel tools for analyzing quantum non-equilibrium dynamics and establishing system stability.
- The findings have direct applications in designing robust quantum algorithms and understanding limitations in quantum optimization.
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