Synthesis of discrete-continuous quantum circuits with multimodal
  diffusion models
Authors: name: Florian Fürrutter, name: Zohim Chandani, name: Ikko Hamamura, name: Hans J. Briegel, name: Gorka Muñoz-Gil

Efficiently compiling quantum operations remains a major bottleneck in
scaling quantum computing. Today's state-of-the-art methods achieve low
compilation error by combining search algorithms with gradient-based parameter
optimization, but they incur long runtimes and require multiple calls to
quantum hardware or expensive classical simulations, making their scaling
prohibitive. Recently, machine-learning models have emerged as an alternative,
though they are currently restricted to discrete gate sets. Here, we introduce
a multimodal denoising diffusion model that simultaneously generates a
circuit's structure and its continuous parameters for compiling a target
unitary. It leverages two independent diffusion processes, one for discrete
gate selection and one for parameter prediction. We benchmark the model over
different experiments, analyzing the method's accuracy across varying qubit
counts, circuit depths, and proportions of parameterized gates. Finally, by
exploiting its rapid circuit generation, we create large datasets of circuits
for particular operations and use these to extract valuable heuristics that can
help us discover new insights into quantum circuit synthesis.