Multiple-layout dynamic programming for DPRQ

Explore storing multiple final qubit layouts for each block–aggregator-node tuple in the DPRQ dynamic program to determine whether retaining more than the single minimum-cost layout can produce better circuit-wide routing optimization.

Background

DPRQ assigns a single final qubit layout to each tuple consisting of a collective communication block and its selected aggregator node. The dynamic program uses the layout associated with the minimum accumulated communication cost when evaluating subsequent blocks.

The paper acknowledges that multiple final layouts for the same block–aggregator-node tuple could potentially lead to better optimization because different layouts may provide better starting configurations for later blocks. However, retaining multiple layouts would increase the space and time complexity of the algorithm, so the paper leaves the exploration of this alternative unresolved.

References

It can be argued that including multiple final qubit layouts for each tuple ($b_{k-1}, n_{k-1}$) might lead to a better optimization, however, it comes at the cost of significant space and time complexity, due to which we include a single best final layout and leave the exploration of storing multiple layouts as future work.

— DPRQ: A Dynamic Programming-based Qubit Routing Algorithm for Collective Communication in Distributed Quantum Computing  (2609.04524 - Vaidya et al., 3 Sep 2026) in Section 3, subsection “DP-based Inter-block Qubit Routing”