This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements of a new basis that we propose as an alternative to Pauli string basis. We call this basis as the Standard Recursive Block Basis, which is constructed using a recursive method, and its elements are permutation-similar to block Hermitian unitary matrices.

翻译：本研究提出一种基于优化的可扩展量子神经网络框架，通过酉矩阵的通用参数化表示来近似$n$量子比特酉算子。该参数化表示由一组新基底的指数乘积构成——我们提出该基底作为泡利字符串基底的替代方案，并将其命名为标准递归块基底。该基底通过递归方法构建，其元素经置换相似变换后等价于块厄米酉矩阵。