The present invention provides systems and methods that facilitate simulating quantum computing and/or provide a language to program a quantum computer. The systems and methods translate received computer instructions (e.g., quantum computer based instructions) to a process algebra (e.g., rho and pi calculus) representation that can be executed by a classical computer to produce a result indicative of a quantum computer. Such mapping can include transformations between vectors, scalars, dual vector and operators in Hilbert space to processes, named processes (quoted names) and quote maps in rho calculus space. Thus, the systems and methods of the present invention can transform a classical computer into a quantum computer simulator. In addition, this process algebra representation can be executed on a quantum computer; thus, the representation can additionally be utilized as a computer language to program a quantum computer.