The efficient quantum circuits of arithmetic operations are important to perform quantum algorithms. To implement efficient matrix operations, we first modify the generalized model of the novel enhanced quantum representation of digital images (GNEQR) to store unsigned and signed integer matrices. Next, we design the circuits of the circuits of quantum addition, quantum modulo addition, quantum subtraction, and quantum modulo subtraction, these operations all keeping two operands unchanged. Then, we propose the circuits of quantum matrix addition, quantum matrix modulo addition, quantum matrix subtraction, and quantum matrix modulo subtraction for the first time. Furthermore, we present a simulation method to verify the correctness of the proposed arithmetic operations of matrix. The results of simulation experiment show that the propose arithmetic operations of matrix are efficient and correct.

中文翻译：

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基于GNEQR的量子矩阵加减法

算术运算的高效量子电路对于执行量子算法很重要。为了实现高效的矩阵运算，我们首先修改了新型增强型数字图像量子表示 (GNEQR) 的广义模型，以存储无符号和有符号整数矩阵。接下来，我们设计了量子加法、量子模加法、量子减法和量子模减法电路的电路，这些操作都保持两个操作数不变。然后，我们首次提出了量子矩阵加法、量子矩阵模加法、量子矩阵减法和量子矩阵模减法电路。此外，我们提出了一种仿真方法来验证所提出的矩阵算术运算的正确性。