A method for generalizing an algorithm configured to synthesize a diagonal product of Pauli rotations to synthesize a product of Pauli rotations comprising X, Y and Z rotations, the method comprising:



Providing a table of p number of rows and m number of columns, where p is a number of qubits and m a number of rotations in the quantum circuit, and where the table comprises X, Y, Z or I entry corresponding to the respective rotations of the qbits;
Determining a pivot row,
and recursively, until all rotations of the product of Pauli rotations are 1-qubit rotations:
Determine a target row,
Conjugate the target row with the pivot row by insertion of predetermined quantum gates on the qubits corresponding to the target row and/or pivot row by calling, at each recursive call, entries of the same type of the pivot row and by always calling first the identity entry.