Editing Glossary (section)

====Brickwork States====
Although cluster states are universal for MBQC, yet we need to tailor these to the specific computation by performing some computational (Z) basis measurements. If we were to use this principle for blind quantum computing, Client would have to reveal information about the structure of the underlying graph state. Thus, for the UBQC protocol, we introduce a new family of states called the Brickwork states which are universal for X − Y plane measurements and thus do not require the initial computational basis measurements. It was later shown that the Z-basis measurements can be dropped for cluster states and hence cluster states are also universal in X-Y measurements.
 <div id="7"> 
 [[File:Brickwork State.jpg|center|thumb|500px|Figure 7: Brickwork State]]</div>
'''Definition 1''' ''A brickwork state Gn×m, where m ≡ 5 (mod 8), is an entangled state of n × m qubits constructed as follows (see also Figure 7):''
#	''Prepare all qubits in state |+i and assign to each qubit an index (i,j), i being a column (i ∈ [n]) and j being a row (j ∈ [m]).''
#	''For each row, apply the operator c-Z on qubits (i,j) and (i,j + 1) where 1 ≤ j ≤ m − 1.''
#	''For each column j ≡ 3 (mod 8) and each odd row i, apply the operator c-Z on qubits (i,j) and (i + 1,j) and also on qubits (i,j + 2) and (i + 1,j + 2).''
#	''For each column j ≡ 7 (mod 8) and each even row i, apply the operator c-Z on qubits (i,j) and (i + 1,j) and also on qubits (i,j + 2) and (i + 1,j + 2).''