t b a b a

4.3 Quantum Scheduling Algorithm
|J1 (m+q) >
|J2 (m+q) >
|JN-1 (m+q) >
|JN (m+q) >
.
.
.
|0 (M(n+q)) >
4.3.1 Information Encoding
.
.
.
Ω
|0 (n+q) >
∆
.
.
.
.
.
.
S (N(m+q))
T (M(n+q))
Cmax (n+q)
Figure 4.1: A quantum circuit to prepare the makespan vector
Let Ω be an operator which given a schedule constructs the running time on each machine
for that schedule. When applied to the equal superposition of all schedules, it produces a
superposition of the running time | T 〉 on each machine for all schedules:
| ����
ST 〉 = Ω(| S〉 | 0〉).
where, | ����
ST 〉 denotes an entangled state of S and T , while the tensor product of S and
T is | ST 〉. Let ∆ be an operator which computes a superposition of the makespan of all
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