Quantum-Walk-Inspired Dynamic Adiabatic Local Search
Abstract
:1. Introduction
2. Background
2.1. Continuous Time Quantum Walk
2.2. Adiabatic Quantum Computing
3. Continuous Time Quantum Walk to Adiabatic Search Mapping
3.1. The Irreconcilability Issue: Constant Gap Catalyst Hamiltonian and Small Norm
3.2. Modified CTQW-Inspired Adiabatic Search
- the scaling factor of Hamiltonian ,
- , catalyst Hamiltonian
- the coefficient function of as .
4. Grover Search to Adiabatic Local Search Mapping
4.1. Adaptive Scheduling
4.1.1. Schedule-Dependent Gap Function
4.1.2. Determining the Sluggish Interval for the Catalyst Hamiltonian
4.1.3. Catalyst Coefficient Functions
5. Experiment and Result
5.1. Modified CTQW-Inspired Adiabatic Search Simulation
- takes Equation (12) and drops the scaling factor as explained in Section 3.2. The adiabatic path is
- replaces the computed catalyst Hamiltonian with an ordinary Z oracle operator and keeps the magnitude M. This was used to address the constant gap irreconcilability issue. We have
- uses as the coefficient function for the catalyst Hamiltonian Z. The adiabatic path is
5.2. Adaptive Adiabatic Local Search Simulation with Various Coefficient Functions
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Time Integration of Adiabatic Local Search
Appendix B. Energy Gap
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Chiang, C.-F.; Alsing, P.M. Quantum-Walk-Inspired Dynamic Adiabatic Local Search. Entropy 2023, 25, 1287. https://doi.org/10.3390/e25091287
Chiang C-F, Alsing PM. Quantum-Walk-Inspired Dynamic Adiabatic Local Search. Entropy. 2023; 25(9):1287. https://doi.org/10.3390/e25091287
Chicago/Turabian StyleChiang, Chen-Fu, and Paul M. Alsing. 2023. "Quantum-Walk-Inspired Dynamic Adiabatic Local Search" Entropy 25, no. 9: 1287. https://doi.org/10.3390/e25091287