  Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum
circuit model, whereby the computation proceeds via measurements on an
entangled resource state. Noise processes are a major experimental challenge to
the construction of a quantum computer. Here, we investigate how noise
processes affecting physical states affect the performed computation by
considering MBQC on a one-dimensional cluster state. This allows us to break
down the computation in a sequence of building blocks and map physical errors
to logical errors. Next, we extend the Matrix Product State construction to
mixed states (which is known as Matrix Product Operators) and once again map
the effect of physical noise to logical noise acting within the correlation
space. This approach allows us to consider more general errors than the
conventional Pauli errors, and could be used in order to simulate noisy quantum
computation.
