quapps Instance Data Set

This is a collection of instances for the problems implemented with our software package quapps. In the quapps package, concrete problem types for quantum optimization are specified. A detailed description of each of the problem types can be found in the corresponding Gitlab repository (https://gitlab.com/quantum-computing-software/quapps). We will therefore not explain the problems in more detail here.

The instantiated optimization problems of this database are based on the quapps package and were created with the implemented random generators. In view of the qubit numbers available in the near future, the number of instances was limited to instances that comprise a maximum of 175 variables. This resulted in different combinations of the defining parameters, such as the size of the graphs or their density:

• Maximum Cut:
  • numbers of nodes 𝑁 ∈ {8, 16, 32, 64, 128, 175},
  • densities 𝑑 ∈ {0.4, 0.6, 0.8} (too low densities lead to non-connected graphs, whereas a density of 1.0 results in a complete graph for which the maximum cut problem for which the maximum cut problem is trivial) and
  • a randomly chosen integer edge weighting between 1 and 5 or no weighting at all,

• Maximum Colorable Subgraph:
  • node numbers 𝑁 ∈ {8, 12, 16},
  • densities 𝑑 ∈ {0.4, 0.6, 0.8} and
  • a number of colors from 3 to the maximum possible for the respective graph (such that the number of variables does not exceed 175),

• Random arbitrary Ising model:
  • qubit numbers 𝑁 ∈ {8, 16, 32, 64, 128, 175},
  • coupling densities 𝑑 ∈ {0.2, 0.4, 0.6, 0.8, 1.0} and
  • random coefficients with an accuracy of 2 decimal places,

• Prime Factorization:
  • two random prime numbers
  • with a number of 3 to 11 bits per prime number
  • which result in a non-trivial optimization problem after preprocessing,

• Traveling Salesperson:
  • node numbers 𝑁 ∈ {8, ..., 13}
  • with random weights on the edges between 1 and 10,

• Graph Partitioning:
  • number of nodes N ∈ {8, 15, 35} (limited since number of variables is product of N and k and shall not surpass 175),
  • densities d ∈ {0.4, 0.6, 0.8} (densities can not be too small so a valid graph can be generated),
  • number of subgraphs k ∈ {2, 3, 5} and
  • weights chosen randomly (uniformly) between 0 and 10 with 2 decimal places,

• Knapsack:
  • number of items I ∈ {32, 100, 175} (number of variables = number of items),
  • maximum value of an item v ∈ {6, 12, 24},
  • maximum weight of an item w ∈ {6, 12, 24} and
  • maximum weight limit of the knapsack W ∈ {20, 40, 80} (range chosen in accordance with maximum weights),

• Minimum k-Union:
  • number of elements E ∈ {40, 80, 120} (limited since number of variables = number of elements + number of subsets),
  • number of subsets S ∈ {40, 45, 50},
  • choices of k ∈ {12, 16, 20} (must not exceed number of subsets but needs to be big enough so that at least one valid covering exists) and
  • maximum subset size s ∈ {28, 34, 40} (must be big enough to ensure existence of valid covering),

• Subset Sum:
  • number of different numbers N ∈ {40, 80, 120, 175} (decides number of variables so limited to 175),
  • maximum number M ∈ {30, 60, 150, 300} (chosen such that for all N, there exists one M thats smaller and one M thats bigger, to allow for both instances with duplicate numbers and instances with unique numbers) and
  • maximum target sum T ∈ {500, 5000, 10000} (big enough so that instances with low N and M can still find a valid sum).

We created 5 different instances for each parameter configuration. This results in a total of 125 Ising, 244 Maximum Colorable Subgraph, 150 Maximum Cut, 124 Prime Factorization, 25 Traveling Salesperson instances, 135 Graph Partitioning, 405 Knapsack, 405 Minimum k-Union and 240 Subset Sum Instances.

Additionally we added 96 Flight-Gate Assignment instances from our publication (https://doi.org/10.1007/978-3-030-14082-3_9):

• Flight-Gate Assignment: 
  • with 3 to 17 flights and
  • correspondingly 3 to a maximum of 17 gates.