A non-recursive universal Quantum turing machine simulation in SequenceL with a post-selection halting scheme

Many quantum programming languages have been recently introduced to create a new tool for expressing quantum algorithms. However, many have failed to formally express themselves as a universal programming language for quantum computation. In this dissertation, the SequenceL language is shown to be universal in two models of quantum computation, the circuit and machine models. A SequenceL quantum interpreter is developed to show universality in the circuit model. A universal quantum Turing machine (UQTM) is introduced using non-recursive computational laws of the functional language, SequenceL with no explicit recursion. The SequenceL UQTM is implemented based on the rules of Bernstein and Vasari’s UQTM. Bernstein and Vasari’s UQTM definition is expanded to include quantum Turing machine with arbitrary run times. Finally, postselection is introduced as a halting scheme for quantum Turing machines.