A Modified Depolarization Approach for Efficient Quantum Machine Learning
Abstract
:1. Introduction
1.1. Contribution
- Depolarization Channel Representation: We propose a modified representation of the depolarization channel for single-qubit quantum states.
- Kraus Operators Configuration: The proposed method contains only two Kraus operators.
- Pauli Matrices Utilization: Unlike the standard approach that uses three Pauli matrices, our channel only uses two, X and Z, Pauli matrices.
- Computational Efficiency: The proposed representation reduces the computational complexity from six to four matrix multiplications for each channel execution.
- Theoretical Verification: We rigorously prove the validity of our proposed Kraus operators and the modified channel.
- Experimental Validation: We empirically tested the proposed channel representation using a QML model on the Iris dataset. We evaluated the model performance across various circuit depths and depolarization rates.
1.2. Organization
2. Preliminaries
2.1. Quantum State and Quantum Gates
2.2. Depolarization Channel Representation
2.3. Quantum Machine Learning
3. Derivation
Alternative Expression of the Depolarizing Channel
4. Experiment
4.1. Quantum Circuit Behavior Analysis under Depolarization Channel up to m Times
4.2. Data Encoding
4.3. Variational Layers
4.4. Training
5. Discussions
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Gate Count | Mean Difference | Standard Deviation | % of Differences above 0.001 |
---|---|---|---|
3 | 0 | 0 | 0% |
8 | 0.00023 | 0.00038 | 6% |
15 | 0.00065 | 0.00106 | 22% |
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Khanal, B.; Rivas, P. A Modified Depolarization Approach for Efficient Quantum Machine Learning. Mathematics 2024, 12, 1385. https://doi.org/10.3390/math12091385
Khanal B, Rivas P. A Modified Depolarization Approach for Efficient Quantum Machine Learning. Mathematics. 2024; 12(9):1385. https://doi.org/10.3390/math12091385
Chicago/Turabian StyleKhanal, Bikram, and Pablo Rivas. 2024. "A Modified Depolarization Approach for Efficient Quantum Machine Learning" Mathematics 12, no. 9: 1385. https://doi.org/10.3390/math12091385