Bridging Pulse and Circuit Levels: A Geometric Framework for Deterministic Error Suppression

Abstract:Quantum errors in noisy environments remain a major obstacle to advancing quantum information technology. Standard quantum error correction requires massive ancillary qubit overhead, motivating the need for hardware-efficient mitigation strategies. In this work, we propose a framework for dynamical quantum error correction at the circuit level, requiring no logical encoding or ancillary qubits. By extending a geometric framework (originally developed for creating dynamical error-correcting gates at the control pulse level) to the discrete dynamics of digital circuits, we map the accumulation of coherent errors to trajectories in a high-dimensional error space. We demonstrate that inserting deterministically optimized twirling gate sequences actively shapes these trajectories, utilizing destructive interference to keep the accumulated error bounded with error scaling $\mathcal{O}(1)$. This deterministic path-shaping suppresses circuit errors fundamentally differently than the stochastic random-walk behavior of standard randomized compiling with error scaling $\mathcal{O}(\sqrt{N})$. Furthermore, we show that this circuit-level dynamical correction synergizes with pulse-level robust control, providing an analytical bridge between continuous noise dynamics and discrete quantum compilation. This research illuminates pathways to achieving highly noise-resistant quantum circuits prior to the era of fault tolerance.

arXiv:2611.06291 [quant-ph]

(or arXiv:2611.06291v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.06291 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1088/2058-9565/ae9b3b Focus to learn more DOI(s) linking to related resources

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