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Table 2 VQA and settings used for the hardware experiments in Figs. 35. An initial parameter \({| +\rangle}^{\otimes N}\) means that the initial angles of all \(R_{y}\) in the first (second) layer of the ansatz are set to 0 (\(\pi /2\)). The last line highlights some key findings from our experiments

From: A case study of variational quantum algorithms for a job shop scheduling problem

  N VQE QAOA VarQITE F-VQE
Ansatz 5
>5
Fig. 2 (p = 2)
Eq. (7) (p = 2)
Fig. 2 (p = 2)
Fig. 2 (p = 2)
Fig. 2 (p = 1)
Initial param.   \({|+\rangle}^{\otimes N}\) uniform in [0,π] \({|+\rangle}^{\otimes N}\) \({|+\rangle}^{\otimes N}\)
Objective   CVaR Eq. (6)
(α = 0.5)
CVaR Eq. (8)
(α = 0.5)
Mean energy Eq. (9) Custom Eq. (13)
Optimizer   COBYLA COBYLA Eq. (12) Eq. (14)
No. shots 5
10
12
16
23
1000



1000



1000



1000
500
550
650
450
Quantum chip 5
10
12
16
23
multiple



multiple



multiple



multiple
ibmq_toronto
ibmq_guadalupe
ibmq_manhattan
ibmq_manhattan
Key findings   Flexible ansatz;
converges slower than F-VQE
Ansatz fixed by problem topology;
poor convergence likely due to noise
Flexible ansatz;
strongly varying performance across runs; converges slower than F-VQE
Flexible ansatz;
fastest, most consistent convergence