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Vanishing correlations in stochastic and bistochastic controlled circuits
Pavel Kos1,2, Bruno Bertini3, Tomaž Prosen1
1University of Ljubljana, Faculty of Mathematics and Physics, Jadranska ulica 19, 1000 Ljubljana, Slovenia.
Physical Review. E
|July 24, 2026
Summary
Stochastic and bistochastic controlled gates in quantum systems simplify complex dynamics. These gates result in vanishing correlations except on the same site, revealing simple structures in quantum correlations.
Area of Science:
- Quantum information science
- Statistical mechanics
- Complex systems
Background:
- Stochastic and bistochastic controlled gates are fundamental in quantum circuits, classical cellular automata, and stochastic circuits.
- Understanding the dynamics and correlation functions of these systems is crucial for quantum information processing and statistical physics.
Purpose of the Study:
- To investigate the spatiotemporal correlation functions arising from circuits with stochastic and bistochastic controlled gates.
- To characterize the general structure of multipoint correlations in such systems.
- To analyze the behavior of autocorrelation functions in large systems.
Main Methods:
- Mathematical analysis of quantum circuit dynamics.
- Derivation and evaluation of two-point and multipoint correlation functions.
- Asymptotic analysis of autocorrelation functions for large system sizes.
Main Results:
- Stochastic and bistochastic controlled gates lead to two-point spatiotemporal correlations that are non-zero only when operators act on the same site.
- For multipoint correlations, the two rightmost operators must act on the same site.
- Autocorrelation functions typically decay exponentially to a value that is exponentially small in system size.
Conclusions:
- A broad class of quantum systems with complex microscopic dynamics exhibits surprisingly simple correlation structures.
- The findings offer insights into the fundamental properties of quantum information processing and complex systems.
- The simplified correlation structure has implications for error correction and algorithm design in quantum computing.
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