t b a b a

A schedule is a tensor product of job-machine vectors:
| Sk〉 = ⊗ 2n
i=1 | e ji
i 〉, 1 ≤ ji ≤ 2 m ,
which includes one job-machine vector for each job. A specific machine may be present in
multiple job-machine vectors, when the schedule requires multiple jobs to be executed on
the same machine, or may not appear in any job machine vectors of the schedule | Sk〉 if
none of the jobs is scheduled on that machine.
The equal superposition of all schedules is:
|x>
| S〉 = 1
√ σ
σ�
| Sk〉, σ = 2 m2n
k=1
|0> pi1
p11 pi2 pi3 pi4
Figure 4.2: A quantum circuit to prepare the job state vectors
First, we need to prepare the job vector | Ji〉 in an equal superposition state which
includes the processing times of job Ji on all machines, as shown in Figure 4.2. We use
51
|Ji>