Characterizing and Benchmarking Dynamic Quantum Circuits

Abstract

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.

Figures (10)

• Figure 1: A dynamic circuit that prepares 2-qubit GHZ state. Note that the information propagates from $q_1$ to $q_2$ through MCM and feed-forward operation.
• Figure 2: Overview of the dynamic circuit benchmarking framework.
• Figure 3: The normalized Rényi-2 entropy $H_2$ of the probability distributions of mid-circuit measurement outcomes on IBM Pittsburgh. A high score means the probability distribution is nearly uniform across all measurement outcomes. The entropy is normalized by the number of classical bits as $H_2 / n_a$. Details of these benchmarks are in Section \ref{['sec:benchmark_suite']}.
• Figure 4: Dynamic circuit benchmark suite in dynamarq.
• Figure 5: Histogram of singular values from PCA on the feature matrix for IBM Pittsburgh (no DD). Results are consistent across all IBM backends with and without DD.