Resource-efficient context-aware dynamical decoupling embedding for arbitrary large-scale quantum algorithms

We introduce and implement GraphDD: an efficient method for real-time, circuit-specific, optimal embedding of dynamical decoupling (DD) into executable quantum algorithms. We demonstrate that for an arbitrary quantum circuit, GraphDD exactly refocuses both quasi-static single-qubit dephasing and crosstalk idling errors over the entire circuit, while using a minimal number of additional single-qubit gates embedded into idle periods. The method relies on a graph representation of the embedding problem, where the optimal decoupling sequence can be efficiently calculated using an algebraic computation that scales linearly with the number of idles. This allows optimal DD to be embedded during circuit compilation, without any calibration overhead, additional circuit execution, or numerical optimization. The method is generic and applicable to any arbitrary circuit; in compiler runtime the specific pulse-sequence solutions are tailored to the individual circuit, and consider a range of contextual information on circuit structure and device connectivity. We verify the ability of GraphDD to deliver enhanced circuit-level error suppression on 127-qubit IBM devices, showing that the optimal circuit-specific DD embedding resulting from GraphDD provides orders of magnitude improvements to measured circuit fidelities compared with standard embedding approaches available in Qiskit.