Quantum Signal-Induced Heap Transform Based Realization of Multi-Qubit Operations

The article presents a new approach to the decomposition of unitary operations by controlled rotations.A new method of quantum signal-induced heap transform based QR decomposition is described.This transform is an analogue of the discrete transform which is generated by a given signal and uses different paths of processing the data.It is shown that among such paths we can find paths that allow constructing efficient quantum circuits for implementing multiqubit unitary gates.The case of real unitary matrices is considered.The proposed approach is described in detail in examples and quantum circuits are presented for 2-qubit operations.The general case of -qubit unitary operations, when 2, is considered similarly.