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arXiv:2606.02018 · IEEE International Conference on Quantum Software (QSW)

Branch-Aware Quantum Constant Propagation for Dynamic Quantum Circuits

Innocenzo Fulginiti, Yanbin Chen

quant-phcs.ETSubmitted Jun 1, 2026• Announced Jun 2, 2026• 0 citations
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Abstract

Compile-time optimization is important for improving the efficiency and reliability of quantum circuits on current noisy hardware. While many existing methods simplify circuits using structural patterns or quantum-state information, most of them target only unitary circuits and do not support dynamic circuits with mid-circuit measurements and classical feedforward. In this work, we present Branch-Aware Quantum Constant Propagation (BQCP), a compile-time analysis for dynamic circuits. BQCP extends Quantum Constant Propagation (QCP) by tracking the classical information produced by mid-circuit measurements together with the corresponding post-measurement quantum states across different execution branches. This enables path-sensitive reasoning inside conditional blocks and more precise information propagation than QCP. To keep the analysis scalable, we bound both the size of the quantum-state representation and the number of tracked branches. Using the information inferred by the analysis, we apply semantics-preserving simplifications to circuit operations. We prove the soundness of both the analysis and the simplifications. Experimental results on both application-driven and synthetic benchmarks show that, on dynamic circuits, our method consistently achieves larger reductions than other existing passes including QCP.

Journal reference
2026 IEEE International Conference on Quantum Software (QSW), pp. 141-151, 2026
DOI
10.1109/QSW72780.2026.00024
Comments
Accepted at IEEE QSW 2026

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Compile-time optimization is important for improving the efficiency and reliability of quantum circuits on current noisy hardware. While many existing methods simplify circuits using structural patterns or quantum-state information, most of them target only unitary circuits and do not support dynamic circuits with mid-circuit measurements and classical feedforward. In this work, we present Branch-Aware Quantum Constant Propagation (BQCP), a compile-time analysis for dynamic circuits. BQCP extends Quantum Constant Propagation (QCP) by tracking the classical information produced by mid-circuit measurements together with the corresponding post-measurement quantum states across different execution branches. This enables path-sensitive reasoning inside conditional blocks and more precise information propagation than QCP. To keep the analysis scalable, we bound both the size of the quantum-state representation and the number of tracked branches. Using the information inferred by the analysis, we apply semantics-preserving simplifications to circuit operations. We prove the soundness of both the analysis and the simplifications. Experimental results on both application-driven and synthetic benchmarks show that, on dynamic circuits, our method consistently achieves larger reductions than other existing passes including QCP.
Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price. Mid-circuit measurements are typically slower and noisier than unitary gates. Furthermore, classical feedforward requires exchanging information between the quantum processor (QPU) and the classical controller, introducing latency that erodes the practical performance of dynamic circuits. 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. 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. We evaluated our framework on randomly generated dynamic circuits, achieving about 50% classical feedforward reduction and even higher reductions in favorable settings.
Dynamic quantum circuits enable adaptive operations through intermediate measurements and classical feedback.Current transpilation toolchains, such as Qiskit and T|ket⟩, however, fail to fully exploit branch-specific simplifications.In this work, we propose recursive branch expansion as a novel technique which systematically expands and refines conditional branches.Our method complements existing transpilers by creating additional opportunities for branch-specific simplifications without altering the overall circuit functionality.Using randomly generated circuits with varying patterns and scales, we demonstrate that our method consistently reduces the depth and gate count of execution paths of dynamic circuits.We also showcase the potential of our method to enable optimizations on error-corrected circuits.
Current quantum computing platforms suffer from readout errors, where faulty measurement outcomes are reported by the device. These errors are particularly harmful in quantum programs that rely on branch statements, where operations in later parts of the program are dynamically determined by mid-circuit measurements. We propose a general protocol for mitigating mid-circuit measurement errors. Our solution works for any number of mid-circuit measurement and feedforward layers without increasing circuit depth or two-qubit gate counts, is efficient under structural assumptions on error channels, and is suitable for immediate application on noisy intermediate-scale quantum devices. We experimentally demonstrate up to a ∼ 60 % reduction in error on superconducting quantum processors across several practically relevant feedforward circuits, including dynamic qubit resets, shallow-depth Greenberger–Horne–Zeilinger state preparation, and multistage quantum teleportation. This work paves the way for more error-resilient adaptive quantum circuits, crucial for current and future quantum computing applications.
Dynamic quantum circuits with mid-circuit measurements (MCMs) and feed-forward operations play a crucial role in various applications, such as quantum error correction and quantum algorithms. With advancements in quantum hardware enabling the implementation of MCM and feed-forward loops, the use of dynamic circuits has become increasingly prevalent. There is a significant need for a benchmarking framework specially designed for dynamic circuits to capture their unique properties, as current benchmarking tools are designed primarily for unitary circuits and cannot be trivially extended to dynamic circuits. We propose dynamarq, a scalable and hardware-agnostic benchmarking framework for dynamic circuits. We collect a set of dynamic circuit benchmarks spanning various applications and propose a broad set of circuit features to characterize the structure of these dynamic circuits. We run them on two IBM quantum processors and the Quantinuum Helios-1E emulator, and propose scalable, application-dependent fidelity scores for each benchmark based on hardware execution results. We perform statistical modeling to identify correlations between circuit features and fidelity scores, and demonstrate highly accurate fidelity prediction using our model. Our model parameters are also transferable across hardware backends and calibration cycles. Our framework facilitates the understanding of dynamic circuit structures and provides insights for designing and optimizing dynamic circuits to achieve high execution fidelity on quantum hardware.
Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit measurements impose significant demands on the quantum hardware due to the required signal analysis and classical feedback loop. This work presents a static circuit optimization algorithm that can substitute some of these measurements with an equivalent circuit with stochastic applications of gates. Our method uses ideas from constant propagation to classically precompute measurement outcome probabilities. Our proposed optimization is efficient, as its runtime scales polynomially on the number of qubits and gates of the circuit.
Dynamic circuits, which incorporate mid-circuit measurements and classically controlled operations, extend the expressive power of quantum programs and are central to applications such as quantum error correction, state preparation, and distributed quantum algorithms. However, their classical simulation is challenging due to the exponential growth of execution branches induced by mid-circuit measurements. In this work, we develop a tensor network approach for simulating dynamic circuits by extending a DMRG-based method for quantum circuit simulation to support dynamic circuit operations. To address the exponential proliferation of execution branches, we introduce and compare two strategies: a single-path stochastic approach that samples individual measurement outcomes, and a multi-path approach that maintains an ensemble of branches. We benchmark these methods on standard dynamic circuits, including the teleportation protocol and GHZ state preparation, as well as on random dynamic circuits. Our analysis explores the trade-offs between simulation accuracy and computational efficiency. These results provide a practical and scalable framework for the classical simulation of dynamic circuits.