Current research
Quantum compilation needs to scale up to i) handle large programs, ii) leverage everything from heterogenous HPC environment, and iii) generalise to non-unitary operations, real-time control flow, error correction etc.
We argue that interpreting quantum compilation as a graph transformation system (GTS) is an elegant, flexible and scalable design for quantum compilers that will enable these goals. My recent contributions (to be pubished with my thesis) resolve the main bottlenecks that GTS-based program optimisation faces, namely the slow rule pattern matching in large rule systems and the difficulty of optimal rule application ordering, a.k.a. the phase ordering problem, as it is known in classical compilation.
The first problem is solved by the introduction of a rule pre-compilation step, during which all rules to be applied are aggregated into a pattern matcher, a finite state automaton-like data structure that can be used to efficiently to traverse a program graph and find all possible rule applications. The paper [2] proves asymptotic bounds on the runtime of this approach for the case of quantum circuits—with a runtime that is independent of the number of rules in the system.
For optimal rule ordering, on the other hand, we propose a distributed search algorithm that relies on the local Church-Rosser theorem to decompose the search space into local problems that can be solved independently. An MPI-based protocol is then used to merge local results into a provably optimal global solution (within the explored search space), using a SAT solver.
Stay tuned for my thesis, coming soon! Oh, and don’t hesitate to reach out in the meantime, always happy to chat.
Publications
- Koch M., Borgna A., Sivarajah S., et al. “HUGR: A Quantum-Classical Intermediate Representation.” Fifth International Workshop on Programming Languages for Quantum Computing, PLanQC 2025. [extended abstract]
- Mondada, L. and Andrés-Martínez P. “Scalable Pattern Matching in Computation Graphs.” 15th International Workshop on Graph Computation Models, GCM 2024_. [arxiv:2402.13065]
- Mondada, L. “Quantum Circuits in Additive Hilbert Space.”, preprint. [2111.01211]
- Corinzia, L., Penna, P., Mondada, L., Buhmann, J. M. (2019). “Exact Recovery for a Family of Community- Detection Generative Models.” IEEE International Symposium on Information Theory, ISIT 2019, 415 – 419. [arxiv:1901.06799]
- Iten, R., Reardon-Smith, O., Mondada, L., Redmond, E., Kohli, R. S., & Colbeck, R. (2019). “Introduction to UniversalQCompiler.” preprint [arXiv:1904.01072]
- Mondada, L., Karim, M.E., and Mondada, F. “Electroencephalography as implicit communication channel for proximal interaction between humans and robot swarms.” Swarm Intelligence 10.4 (2016): 247-265 [pdf].
Other past research and essays
- Abstract Primitives for Quantum Computation. [Term paper]
- Simulating continuous-variable quantum computations on discrete devices. [MFoCS dissertation]
- An exploration of the meaning of Born’s rule. [miniproject]