量子神经网络通用逻辑操作器的设计与实现

Design and Implementation of a Universal Logic Operator for Quantum Neural Networks

  • 摘要: 本文设计一个2输入16输出量子相位神经网络,完成实现一个16种逻辑操作器,并通过参数化量子线路进行验证。所设计的量子相位神经网络由2个实数输入、量子态相位编码函数和16个量子逻辑操作单元组成,其中每一个量子逻辑操作单元由包含2个量子位与2个辅助量子位作为输入的参数化量子线路实现。所设计的参数化量子线路仅包含5个可调权相位,采用相位可调的R_y门实现相位旋转,1个受控门R_y和1个Toffoli门来实现多量子位的相位叠加,最终通过计算网络输出\left| 1 \right\rangle 相位的正弦值的平方,也就是输出量子态在\left| 1 \right\rangle 的概率,得到该逻辑操作器的实数输出,实现16种逻辑运算中的任意一种逻辑操作。本文采用梯度下降法和自适应学习速率推导出可调权相位的修正学习训练算法,并且在基于Qiskit平台构建的参数化量子线路上实现,并在结构复杂度以及实现精度上与其他网络进行性能对比,为多输入/多输出量子相位神经网络的实际应用开辟了新的应用途径。

     

    Abstract: A 2-input 16 output quantum phase neural network (QPNN) is designed to implement 16 types of logic operators and is verified by the parameterized quantum circuits. The proposed QPNN comprises two real-valued inputs, a quantum state phase encoding function and 16 quantum logic operator units. Each quantum logic operator unit is realized through a parameterized quantum circuit with two input qubits and two auxiliary qubits. The circuit employs only five adjustable weight phases, which utilizes phase-tunable R_y gates for phase rotation, a controlled-R_y gate, and a Toffoli gate to achieve multi-qubit phase superposition. The real-valued output of the logic operator is derived by computing the square of the sine function value of the output phase, which corresponds to the probability of the quantum state in \left| 1 \right\rangle , thereby enabling any of the 16 logical operations. This paper also develops a learning algorithm with adjustable weight phases based on the gradient descent method and adaptive learning rate. The proposed work is implemented and validated on the parameterized quantum circuits constructed by using the Qiskit platform and compared with other networks in terms of structural complexity and implementation accuracy. This work opens up new possibilities for the practical application of multi-input/multi-output quantum phase neural networks, particularly through the Qiskit-based implementation of parameterized quantum circuits.

     

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