Compile-Time Simplification of Classically Controlled Operations in Dynamic Circuits

Dynamic circuits enable decision-making during execution by conditioning subsequent operations on measurement outcomes obtained at runtime. By combining mid-circuit measurements with classical controlled operations, they allow quantum programs to adapt their behavior during execution, increasing expressiveness compared to static circuits that follow a fixed sequence of operations. This flexibility supports a broad range of applications, including qubit reuse, quantum teleportation, and distributed quantum computing. However, these benefits come at a cost. Mid-circuit measurements are typically slower and noisier than unitary gates, and classically controlled operations require a feedback loop between the quantum processor and the classical controller, introducing latency that can degrade practical performance.

We propose a compile-time optimization framework that reduces the use of classical controls in dynamic circuits while preserving their semantics. At its core, the framework uses a static analysis that symbolically executes the circuit by propagating classical information alongside the quantum state. By combining this classical–quantum information with the Probabilistic Circuit Model extended with probabilistic controls that emulate classical feedforward, we obtain an intermediate probabilistic representation of the dynamic circuit. In this representation, mid-circuit measurements and classically controlled operations can be removed or rewritten as purely unitary operations and probabilistic components.
The optimization pass proceeds in two phases. First, the input dynamic circuit is transformed into a semantically equivalent probabilistic circuit in which classical feedforward is encoded through probabilistic constructs. Second, this probabilistic representation is compiled into executable circuit instances by replacing probabilistic components with standard quantum operations.

We evaluated our framework on randomly generated dynamic circuits, achieving about $50\%$ classical feedforward reduction and even higher reductions in favorable settings.
Compared to existing compile-time optimizations that target only mid-circuit measurements, our method applies to a broader class of dynamic circuits expressible in modern quantum programming languages.

---

Contributors:

• Yanbin Chen
• Christian B. Mendl
• Helmut Seidl