Table 1 Summary of results for using the QAOA to distinguish non-isomorphic graph sets.

From: Efficient parallelization of tensor network contraction for simulating quantum computation

Class or pair of graphs

Number of nodes

QAOA depth giving full separation

Contraction cost

Miyazaki I and II

20

4

10.1

Praust I and II

20

4

10.5

Cai–Fürer–Immerman graphs I and II

40

6

15.4

All 4,060 non-isomorphic 3-regular graphs on 16 nodes51

16

4

8.7

All 41,301 non-isomorphic 3-regular graphs on 18 nodes51

18

4

9.3

All 10 non-isomorphic graphs in the SRG 26,10,3,4 family52

26

3

12.8

  1. Experiments were conducted on the 20-node Miyazaki graphs, 20-node Praust graphs, 40-node Cai–Fürer–Immerman graphs, all non-isomorphic 3-regular graphs on 16 and 18 nodes, and all non-isomorphic (26, 10, 3, 4) strongly regular graphs. The number of nodes, the minimum QAOA depth to tell all of the graphs apart, and the average contraction cost for one graph, are listed. Only the Cai–Fürer–Immerman graph pair requires index slicing, as the graphs contain many nodes and it takes a deep QAOA circuit to tell the two graphs apart.
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