A vectorial Boolean function takes multi-bit input and produces a multi-bit output. According to the input parameters, a vectorial Boolean function can be linear or non-linear. Non-linear vectorial Boolean functions have high importance in information theory and cryptology. Finding a linear approximation of a non-linear vectorial Boolean function is of high significance in these areas. Assuming that the quantum access to a vectorial Boolean function is provided, we present a quantum computing approach which can find the best linear approximation of the non-linear vectorial Boolean functions. The presented quantum approach is exponentially better than any known solution on the factors of querying the function, quantum circuit depth and memory requirements.

向量布尔函数采用多位输入并产生多位输出。根据输入参数，矢量布尔函数可以是线性的或非线性的。非线性矢量布尔函数在信息论和密码学中具有很高的重要性。在这些领域中，找到非线性矢量布尔函数的线性逼近意义重大。假设提供了对矢量布尔函数的量子访问，我们提出了一种量子计算方法，该方法可以找到非线性矢量布尔函数的最佳线性逼近。在查询功能，量子电路深度和存储要求的因素上，提出的量子方法比任何已知的解决方案都好几倍。