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Information theoretical analysis of quantum optimal control.
1Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|July 18, 2014
Summary
Efficient classical information enables accurate quantum system control. This study shows optimal control of many-body quantum systems, especially 1D entangled dynamics, is feasible with finite precision, with implications for quantum computing and error correction.
Area of Science:
- Quantum mechanics
- Quantum control theory
- Computational complexity
Background:
- Accurate manipulation of quantum system dynamics is crucial for quantum technologies.
- The relationship between classical information and quantum control feasibility is not fully understood.
- Efficiently solving optimal control problems in complex quantum systems remains a challenge.
Purpose of the Study:
- To investigate the connection between classical information and the feasibility of precise quantum system manipulation.
- To determine if efficient classical representations of quantum dynamics allow for efficient optimal control.
- To analyze the impact of noise on these control processes.
Main Methods:
- Analysis of the relationship between classical information and quantum dynamics.
- Development of criteria for efficient classical representation of quantum system dynamics.
- Formulation and analysis of optimal control problems for many-body quantum systems.
- Derivation of bounds for control process duration based on control pulse bandwidth (continuous Solovay-Kitaev theorem).
- Quantification of noise effects on control precision and efficiency.
Main Results:
- An efficient classical representation of quantum dynamics guarantees efficient solvability of optimal control problems with finite precision.
- One-dimensional slightly entangled quantum dynamics can be efficiently controlled.
- A bound on the minimal time for optimal control is established, related to control pulse bandwidth.
- The study quantifies the impact of noise on the controllability and precision of quantum systems.
Conclusions:
- Classical information plays a pivotal role in enabling efficient and accurate quantum control.
- The findings suggest practical pathways for controlling complex quantum systems, particularly in one-dimensional settings.
- The developed bounds and noise analysis provide essential insights for designing robust quantum control protocols.
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