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Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics.
Srinivasan S Iyengar1,2, Anup Kumar1, Debadrita Saha1
1Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States.
Journal of Chemical Theory and Computation
|September 13, 2023
Summary
A new quantum dynamics formalism unifies diverse quantum algorithms and natural phenomena. This framework reveals parallels between quantum computing algorithms and correlated proton behavior in water, highlighting universal principles in quantum systems.
Area of Science:
- Quantum Information Science
- Quantum Dynamics
- Computational Physics
Background:
- Quantum algorithms like Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor offer powerful computational capabilities.
- Quantum dynamics is conventionally studied using tensor networks.
- Understanding the fundamental connections between algorithms and natural phenomena can lead to new insights.
Purpose of the Study:
- To introduce a general formalism for quantum dynamics.
- To demonstrate how this formalism unifies various quantum algorithms and tensor network approaches.
- To explore the parallels between quantum algorithms and natural quantum phenomena.
Main Methods:
- Development of a unifying mathematical framework for quantum dynamics.
- Application of the formalism to known quantum algorithms (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, Shor).
- Analysis of quantum dynamics in biological and materials systems, specifically correlated proton behavior in water wire systems.
Main Results:
- The proposed formalism successfully subsumes multiple quantum algorithms and the tensor network approach.
- The framework reveals underlying similarities between distinct quantum algorithms.
- A direct parallel is drawn between the structure of Shor's algorithm and the correlated behavior of protons in water wire systems.
Conclusions:
- A general formalism for quantum dynamics provides a unified perspective on quantum computation and natural quantum systems.
- The connection between quantum algorithms and natural phenomena, exemplified by Shor's algorithm and proton behavior, suggests universal principles.
- This unified framework can foster new research at the intersection of quantum computing, physics, chemistry, and biology.
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