Measurement-Based Quantum Circuits Model

Quantum circuits are still widely used as a convenient formalism for describing quantum computation, and they provide a framework for the structure of quantum algorithms and the physical realization of quantum computers. Measurement-based quantum computation has emerged from the physics community as a new apporach to quantum computation. This paper attempts to address a measurement-based quantum circuits model in terms of the measurement calculus and distributed quantum computation. We consider how the measurement results influence the unitary evolution and their relations. We discuss that measurement-based quantum circuits act on the pure states and mixed states, where the maixed states from some pure states ensemble. Then, we define a union for two primitive actions in terms of the pure states, and prove that the union of any two primitive actions is a primitive action, and it can be generalized to the mixed states. Since the union and the connection are closed for the primitive actions, then we can define the promitive actions of the measurement-based quantum circuits medel. Finally, based on these discussions, we prove that any measurement-based quantum circuits model is equivalent to quantum operation, and give an example to explain it. It is shown that quantum operation can describe any measurement-based quantum computation.