Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.
Wu, Shixin, "Computer Program Simulation of a Quantum Turing Machine with Circuit Model" (2021). Mathematical Sciences Technical Reports (MSTR). 177.