Reordering Decision Diagrams for Quantum Computing Is Harder Than You Might Think

Abstract

Decision diagrams have proven to be a useful data structure in both, conventional and quantum computing, to compactly represent exponentially large data in many cases. Several approaches exist to further reduce the size of decision diagrams, i.e., their number of nodes. Reordering is one such approach to shrink decision diagrams by changing the order of variables in the representation. In the conventional world, this approach is established and its availability taken for granted. For quantum computing however, first approaches exist, but could not fully exploit a similar potential yet. In this paper, we investigate the differences between reordering decision diagrams in the conventional and the quantum world and, afterwards, unveil challenges that explain why reordering is much harder in the latter. A case study shows that, also for quantum computing, reordering may lead to improvements of several orders of magnitude in the size of the decision diagrams, but also requires substantially more runtime.

Publication
In Conference on Reversible Computation
Lukas Burgholzer
Lukas Burgholzer
PhD Student

My research interests include design automation for quantum computing, decision diagrams, and in particular equivalence checking of quantum circuits