Efficiency of MPO–MPO contractions in QTT parquet solvers

Develop more efficient algorithms for matrix product operator–matrix product operator contractions within QTT-based implementations of the Bethe–Salpeter and parquet equations to reduce computational scaling and alleviate the current D^4 bottleneck.

Background

In the presented framework, the costliest operations are MPO–MPO contractions used to implement matrix multiplications in the Bethe–Salpeter equations. Their quartic scaling in the maximum bond dimension makes them the dominant computational bottleneck.

Improving contraction algorithms—potentially with cross-interpolation-based truncations or structure-exploiting schemes—would materially expand the practical range of QTT parquet computations.

References

To pursue such a strategy and optimize its efficiency, further methodological developments will be required to address some open questions: How can MPO-MPO contractions (the current bottleneck) be performed more efficiently?

— Two-particle calculations with quantics tensor trains: Solving the parquet equations  (2410.22975 - Rohshap et al., 2024) in Appendix: Model extensions