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Limitations are imposed by the strong Church thesis on quantum computers. Many hypothetical machines have been realized, however these machines cannot be constructed in reality. Church’s thesis requires these machines to be physical, therefore these hypothetical machines cannot represent a quantum computer that satisfies the strong Church thesis. Church’s thesis originally defined the guideline for hypothetical quantum computers used to realize quantum algorithms such as Shor’s algorithms for factorization and discrete logarithms. Specifically, Shor’s algorithms utilize the quantum gate array model to simulate a quantum computer with an arbitrary hamiltonian. There are many other quantum models, including the adiabatic quantum computer and one-way quantum computer. When preforming a calculation the model that best of best fit is selected.

Computational ability is limited by the space and time requirements of a process, such as an algorithm. While in classical computation we only are limited by space and time, quantum computation introduces a new limiting variable: precision. Precision is introduced inherently from superposition of states in quantum mechanics, and is a measure of the accuracy of a computation. This precision is governed by the Heisenberg uncertainty principle which similarly governs measurements in quantum mechanics. Introduction of precision into quantum computations is thought to enable quantum computers to solve problems in polynomial time when on a classical computer, the solution to these problems are nondeterministic polynomial time or worse.