Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure
Abstract
1. Introduction
2. Quantum Competitive Learning
3. Qubits and Quantum Gates
3.1. Qubit
3.2. Quantum Gates
4. Methodology
- Prepare two copies of the two-qubit state given by Equation (2) as follows:
- gate is applied between the second and the forth qubits, respectively, followed by the rotation R gate as follows:
5. The proposed Quantum Classification Algorithm Based on Competitive Learning and Entanglement Measure: Case Study
Algorithm 1 The proposed Quantum Classification Algorithm based on Competitive Learning and Entanglement Measure (QCPNN). |
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5.1. Case Study
5.1.1. Quantum-Storing Layer Using Zhou’s Storage Model
- Step 1: The quantum system is initialized by the three registers , and as = . Assuming that the input state is given by , where the first pattern in Equation (9) is considered, so the initial state can be described as = .
- Step 2: = where is the toffli gate (Equation (1)).
- Step 3: =
- Step 4: =
- Step 6: =
- Step 7: =
- Step 8: =
5.1.2. Classification an Input Using the Proposed Algorithm
- Initialization Step:Here, the input register is , is the memory register that holds the prototypes patterns and its state is given by Equation (11), and is initialized by the state . Due to the input, test, pattern has two well known values in the first and third qubits, so . Therefore, the state of the system is described as follows:
- Apply the competitive detection operator between the input register and the prototype register as .
- Apply the Toffoli-gate between qubits of the register and the qubit as control qubits and target qubit, respectively.Hence, the state of the two-qubit system is
- Repeat the steps 1, 2 and 3 to get another decoupled copy of the state .
- Apply the operator on the state yields the state:Here, it is obvious that the probability of the state , , or is non-zero, so according to Equation (7) the concurrence value . Then, the test pattern belongs to the class label “1”.
6. Application
7. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Thermal barrier flow low | |
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Charging pump flow low | |
No.1 seal leak off flow low | |
Bearing temperature high | |
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Thermal barrier temperature high |
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Zidan, M.; Abdel-Aty, A.-H.; El-shafei, M.; Feraig, M.; Al-Sbou, Y.; Eleuch, H.; Abdel-Aty, M. Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure. Appl. Sci. 2019, 9, 1277. https://doi.org/10.3390/app9071277
Zidan M, Abdel-Aty A-H, El-shafei M, Feraig M, Al-Sbou Y, Eleuch H, Abdel-Aty M. Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure. Applied Sciences. 2019; 9(7):1277. https://doi.org/10.3390/app9071277
Chicago/Turabian StyleZidan, Mohammed, Abdel-Haleem Abdel-Aty, Mahmoud El-shafei, Marwa Feraig, Yazeed Al-Sbou, Hichem Eleuch, and Mahmoud Abdel-Aty. 2019. "Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure" Applied Sciences 9, no. 7: 1277. https://doi.org/10.3390/app9071277
APA StyleZidan, M., Abdel-Aty, A.-H., El-shafei, M., Feraig, M., Al-Sbou, Y., Eleuch, H., & Abdel-Aty, M. (2019). Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure. Applied Sciences, 9(7), 1277. https://doi.org/10.3390/app9071277