A programming language combining quantum and classical control

Abstract:The two main notions of control in quantum programming languages are often referred to as "quantum control" and "classical control". With the latter, the control flow is based on classical information, potentially resulting from a quantum measurement, and this paradigm is well-suited to mixed state quantum computation. Whereas with quantum control, we are primarily focused on pure quantum computation and there the "control" is based on superposition. The two paradigms have not mixed well traditionally and they are almost always treated separately. In this work, we show that the paradigms may be combined within the same system. The key ingredients for achieving this are: (1) syntactically: a modality for incorporating pure quantum types into a mixed state quantum type system; (2) operationally: an adaptation of the notion of "quantum configuration" from quantum lambda-calculi, where the quantum data is replaced with pure quantum primitives; (3) denotationally: suitable (sub)categories of Hilbert spaces, for pure computation and von Neumann algebras, for mixed state computation in the Heisenberg picture of quantum mechanics.

Extended version of this https URL and related to the PhD thesis at arXiv:2406.07216

Logic in Computer Science (cs.LO); Programming Languages (cs.PL); Quantum Physics (quant-ph)

arXiv:2511.22537 [cs.LO]

(or arXiv:2511.22537v2 [cs.LO] for this version)

https://doi.org/10.48550/arXiv.2511.22537 Focus to learn more arXiv-issued DOI via DataCite

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