Programming with Quantum-Controlled Quantum Channels
Kengo Hirata , Takeshi Tsukada
arXiv: 2607.15873
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.
A naive way to control a program by a qubit is by means of a controlled operation. Given an operation $F$, this amounts to considering an operation that behaves as $F$ when the control qubit is $|1\rangle$, and as the identity operation when the control qubit is $|0\rangle$. This idea works well when $F$ is a unitary operations, but it is not well-defined for a general quantum channel. By contrast, the quantum SWITCH is free from the well-definedness issue. This contrast leads to the key insight of this paper: controlled operations and the quantum SWITCH should be regarded as different kinds of quantum control mechanisms.
Building on this insight, we develop a novel quantum programming language with quantum control and measurement that can express the quantum SWITCH over quantum channels. Using a semantic analysis based on program transformations, we identify the source of the ill-behavedness of controlled operations as the \emph{correspondence problem}: a lack of coordination between the measurements performed in the then- and else-branches of quantum conditional branching. We address this problem 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.
Talks
LIQCS 2026
Authors: Kengo Hirata, Takeshi Tsukada.
Date: 19 Jun 2026.
Venue: LIQCS 2026. INRIA, Paris.