Scalable quantum error mitigation with phase-cycled dynamical decoupling

TL;DR

This work tackles the challenge of overestimating qubit coherence times caused by control errors in dynamical decoupling by introducing Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method. By exploiting abelian group structure via Sylvester Hadamard matrices, HPC achieves linear circuit-depth scaling while suppressing erroneous dynamics, enabling reliable T2 measurements and state-protection across diverse qubit platforms. The authors demonstrate HPC on ensemble molecular spins and NV centers, as well as on single trapped-ion and superconducting qubits, achieving near-quantitative effective state fidelity and substantial improvements in decoherence-time assessments. The approach promises to enhance QEM integration with DD, facilitating robust quantum technologies under realistic noisy hardware and helping guide sequence design, quantum sensing, and NISQ-era computing.

Abstract

The realization of quantum technologies in the Noisy Intermediate-Scale Quantum era is severely constrained by qubit decoherence and control errors, presenting fundamental challenges to achieving quantum advantages. Dynamical decoupling is a widely used, powerful technique for decoherence error suppression. However, it is susceptible to control errors, making non-robust sequences like UDD impractical to implement and robust ones like CPMG to significantly overestimate decoherence times. This overestimation issue remains largely unexplored in the past few decades, leading to many reports of exceptionally long yet plausible decoherence times across various qubit platforms. Here, we construct Hadamard phase cycling as a non-Markovian quantum error mitigation method for dynamical decoupling. This method exploits group structure to design phase configurations of equivalent ensemble quantum circuits, effectively eliminates circuit outputs generated from erroneous dynamics, and scales linearly with circuit depth. Harnessing its error mitigation capability for ensemble solid-state electron spin qubits embedded in paramagnetic molecules and nitrogen-vacancy centers in diamond enables accurate acquisition of decoherence times. Applying Hadamard phase cycling on single trapped ion and superconducting transmon qubits effectively preserves their state fidelity during dynamical decoupling. The integration of scalable quantum error mitigation and suppression would facilitate the development of quantum technologies with noisy qubits and control hardware.

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