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Published on: August 2, 2019
Trotter transition in Bardeen-Cooper-Schrieffer pairing dynamics
Aniket Patra1, Emil A Yuzbashyan2, Boris L Altshuler3
1Institute for Basic Science, Center for Theoretical Physics of Complex Systems, Daejeon 34126, Republic of Korea.
Physical Review. E
|February 20, 2026
Summary
Trotterization in quantum computation can lead to chaos. This study reveals a "Trotter transition" where dynamics shift from weak chaos to short correlations, impacting thermalization.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Computation
Background:
- Thermalization is crucial for quantum computation.
- Trotterization is a standard technique in gate-based quantum computation.
- Understanding Trotterization-induced chaos is vital for quantum algorithm stability.
Purpose of the Study:
- To investigate universal aspects of thermalization driven by Trotterization.
- To analyze the chaotic dynamics induced by Trotterization in a specific quantum model.
- To characterize the influence of Trotterization time step on chaos quantifiers.
Main Methods:
- Utilized the reduced-Bardeen-Cooper-Schrieffer model.
- Characterized dynamics using Lyapunov spectrum and Kolmogorov-Sinai entropy.
- Numerically fitted maximum Lyapunov exponent data to derive scaling laws.
Main Results:
- Observed a Trotter transition at a critical time step τ_{c}≈sqrt[N].
- Identified distinct dynamics regimes: weakly chaotic (τ≪τ_{c}) and short temporal correlations (τ≫τ_{c}).
- Derived two scaling laws for Lyapunov exponent, with the large τ limit matching the kicked top map.
Conclusions:
- Trotterization introduces a transition in chaotic dynamics with implications for thermalization.
- The findings are relevant for current quantum computers and suggest new research avenues.
- The study opens possibilities for probing complex quantum observables across the Trotter transition.
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