  In the framework of quantum computational tensor network, which is a general
framework of measurement-based quantum computation, the resource many-body
state is represented in a tensor-network form, and universal quantum
computation is performed in a virtual linear space, which is called a
correlation space, where tensors live. Since any unitary operation, state
preparation, and the projection measurement in the computational basis can be
simulated in a correlation space, it is natural to expect that fault-tolerant
quantum circuits can also be simulated in a correlation space. However, we
point out that not all physical errors on physical qudits appear as linear
completely-positive trace-preserving errors in a correlation space. Since the
theories of fault-tolerant quantum circuits known so far assume such noises,
this means that the simulation of fault-tolerant quantum circuits in a
correlation space is not so straightforward for general resource states.
