Scalable Quantum Circuits for N-Qubit Unitary Matrices

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 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.