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Uncertainty Relations in Implementation of Unitary Operations
Hiroyasu Tajima1, Naoto Shiraishi2, Keiji Saito2
1Department of Communication Engineering and Informatics, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan.
Physical Review Letters
|September 29, 2018
Summary
Implementing accurate unitary operations requires a trade-off with quantum energy fluctuations in external apparatus. Greater accuracy necessitates larger energy fluctuations for precise quantum control.
Area of Science:
- Quantum mechanics
- Quantum information science
- Physics of computation
Background:
- Unitary operations are fundamental for quantum computation and information processing.
- Implementing precise unitary time evolution is crucial for quantum technologies.
- Understanding the physical constraints on implementing quantum operations is an ongoing challenge.
Purpose of the Study:
- To investigate the underlying mechanism and fundamental limitations in implementing unitary operations.
- To explore the relationship between implementation accuracy and quantum energy fluctuations.
- To establish trade-off relations governing the fidelity of unitary operations.
Main Methods:
- Modeling the implementation of unitary operations as a physical phenomenon arising from system-apparatus interaction.
- Analyzing the constraints imposed by quantum fluctuation of energy in the external apparatus.
- Deriving theoretical trade-off relations between accuracy and energy fluctuation.
Main Results:
- A direct link is established between the accuracy of unitary operation implementation and quantum energy fluctuations.
- The study reveals that achieving high accuracy in unitary operations inherently requires significant energy fluctuation in the apparatus.
- Trade-off relations quantifying this limitation are clearly demonstrated.
Conclusions:
- Accurate unitary operations are fundamentally limited by quantum energy fluctuations in the controlling apparatus.
- The findings highlight a critical trade-off that must be considered in the design of quantum computing architectures.
- Future quantum control strategies may need to account for and potentially mitigate these inherent quantum fluctuations.
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