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This research introduces a typed lambda calculus that formally enforces causality constraints to distinguish between physically realizable and theoretically impossible quantum processes. By leveraging intuitionistic BV logic, the work provides a rigorous framework for verifying the correctness of higher-order quantum programs before implementation. This advancement is critical for establishing trust in future quantum systems by ensuring operations adhere strictly to physical laws rather than relying on empirical observation alone.
New Programming Language Enforces Causality in Quantum Programs

Indefinite causal order is a characteristic phenomenon in quantum computation, with examples including the quantum SWITCH and the OCB process. This paper studies a causality issue in a higher-order setting, proposing a typed lambda calculus with quantum control and its categorical semantics, equipped with a type system based on intuitionistic BV logic to enforce causality.
Kengo Hirata and Takeshi Tsukada are developing a new programming language to address a fundamental question in quantum computing: what separates physically possible processes from those that remain…
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