Method for synthesizing product of pauli rotations in a quantum circuit and process for synthesizing quantum circuits for trotter-suzuki n-order expansion

Method for synthesizing product of Pauli rotations, wherein said product of Pauli rotations comprises at least two different types of X, Y, and/or Z n-qbits Pauli rotations and identities (I), said 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 a quantum circuit, and where the table comprises X, Y, Z or I entry corresponding to the respective rotations of the qubits;
• determining a pivot row as being a first row comprising a maximum number of a same type of X, Y, Z or I entry;
• performing a subset of steps recursively, until all qubits perform only 1-qubit-rotation, the subset of steps comprising:
• determining if the pivot row comprises at least one identity entry;
• determining a target row among remaining rows, said target row containing a maximum of non-identity entries interacting with the entries of the pivot row;
• conjugating said pivot row and said target row by inserting a predetermined type of quantum gates on their respective qubits in order to bring the X, Y or Z entry of at least the pivot row to I entry;
• and
• rewriting the table according to a result of the conjugation, by replacing the X, Y and/or Z entry of at least the pivot row by an identity entry;
• and
• returning the rewritten table,
• wherein if the pivot row is determined to comprise at least one identity entry, the pivot row is determined as being a second row having the maximum number of the same type of X, Y, Z, or I entry, and being different from the first row, and
• wherein if the pivot row is determined to not comprise at least one identity entry, the determination of a target row is performed directly after.