  Measurement-based quantum computation utilizes an initial entangled resource
state and proceeds with subsequent single-qubit measurements. It is implicitly
assumed that the interactions between qubits can be switched off so that the
dynamics of the measured qubits do not affect the computation. By proposing a
model spin Hamiltonian, we demonstrate that measurement-based quantum
computation can be achieved on a thermal state with always-on interactions.
Moreover, computational errors induced by thermal fluctuations can be corrected
and thus the computation can be executed fault-tolerantly if the temperature is
below a threshold value.
