Programming with Quantum Controlled Quantum Channels
- Authors: Kengo Hirata, Takeshi Tsukada.
- Date: 19 Jun 2026.
- Venue: LIQCS 2026. INRIA, Paris.
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Abstract
In contrast to a classical bit, which can only take the value 0 or 1, its quantum counterpart—a qubit—can exist in a superposition of $0$ and $1$. This is a superposition of data values, naturally raising the question of whether one can superpose not only data but also programs. For example, a particular superposition of programs, known as the quantum SWITCH, has attracted much attention, and its implementations and computational advantages have been studied extensively within the physics community.
Programming languages with quantum control typically restrict the target of quantum control to unitary operations; as a consequence, they cannot express the quantum SWITCH, which applies to quantum channels—the broader class that includes measurements. There are some proposals of languages with both measurement and quantum control, but these languages cannot describe the quantum SWITCH and suffer from an ill-behavedness issue of the semantics.
This paper introduces a novel quantum programming language with both quantum control and measurement that can express the quantum SWITCH over quantum channels. Using a semantic analysis, we identify the source of the ill-behavedness as the correspondence problem: a lack of coordination between the then- and else-branches of a quantum conditional branching. We address this with a linear type system that enforces alignment of the quantum operations used in the two branches, yielding a well-behaved language capable of expressing the quantum SWITCH.