# The classical simulation of 2D graph state and the measurement based quantum computation

In my former post on Physics SE I deduced a contradiction in the classical simulation of 2D graph state and the classical simulation of general measurement-based quantum computation.

In Norbert's answer, he mentioned that the serial measurements on the graph state cannot be classically simulated.

This might be the right answer if we admit that a general quantum computation cannot be efficiently simulated classically. Especially if the quantum computation is not measurement based but rather a normal quantum circuit based implementation, since even the initial state can be simulated classically, the evolution of the state may change the state and the entanglement pattern so that it does not fulfill a certain criterion for the classical simulation.

But for measurement based QC, the measurement is carried out on each individual qubit and the measurement on one qubit will not change the state of another qubit. So the sequential measurements on each qubit can all be classically simulated. Then the contradiction is still there.

I am sure there must be something wrong with my deduction. Please help me to find it.

• @XXDD Yes, but the measurement results have to be globally consistent. For example, if you measure the two qubits in $|01\rangle-|10\rangle$ in the same basis,, you must get opposite answers. – DaftWullie Oct 29 '18 at 16:03