Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate-application probabilities based on the strengths of Hamiltonian terms, as measured by the Schatten-$\infty$ norm. However, relying solely on the Schatten-$\infty$ norm to define sampling distributions may not be optimal, especially for continuous-variable and hybrid-variable systems involving unbounded operators, where quantifying Hamiltonian strengths is challenging. In this work, we propose an adaptive randomized compilation algorithm that dynamically updates sampling weights via low-order moment measurements of Hamiltonian terms, assigning higher probabilities to terms with greater uncertainty. This approach improves accuracy without significantly increasing gate counts and extends randomized compilation to continuous-variable and hybrid-variable systems by addressing the difficulties in characterizing the strengths of unbounded Hamiltonian terms. Numerical simulations demonstrate the effectiveness of our method.

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• Quantum algorithms
• Quantum simulation