Improved quantum circuit modelling based on Heisenberg representation

Heisenberg model allows a more compact representation of certain quantum states and enables efficient modelling of stabilizer gates operation and single-qubit measurement in computational basis on classical computers. Since generic quantum circuit modelling appears intractable on classical computers, the Heisenberg representation that makes the modelling process at least practical for certain circuits is crucial. This paper proposes efficient algorithms to facilitate accurate global phase maintenance for both stabilizer and non-stabilizer gates application that play a vital role in the stabilizer frames data structure, which is based on the Heisenberg representation. The proposed algorithms are critical as maintaining global phase involves compute-intensive operations that are necessary for the modelling of each quantum gate. In addition, the proposed work overcomes the limitations of prior work where the phase factors due to non-stabilizer gates application was not taken into consideration. The verification of the proposed algorithms is made against the golden reference model that is constructed based on the conventional state vector approach.