通过可检测性引理实现量子Gibbs采样
Quantum Gibbs sampling through the detectability lemma
AI总结：
本文利用可检测性引理改进Gibbs态制备，设计无需模拟主方程的新型方法，降低计算成本，并结合量子奇异值变换实现无 frustrations Hamiltonian 的基态投影算子，取得谱间隙依赖的二次加速。
摘要：
Gibbs态制备是量子计算中的重要子程序。本文利用可检测性引理改进Gibbs态制备。具体而言，我们设计了不依赖模拟主方程的新型Gibbs态制备方法，从而避免其开销。对于由M个项组成的局部主方程，这种方法将成本降低了O(M)倍。我们还结合可检测性引理算子和量子奇异值变换，实现无frustration Hamiltonian 的基态投影算子，从而在谱间隙依赖上取得二次加速。将此方法应用于局部交换哈密顿量的Gibbs态主方程，实现了在主方程谱间隙依赖上的二次改进。
英文摘要：
Gibbs state preparation is an important subroutine in quantum computing. In this work we use the detectability lemma to improve Gibbs state preparation. Specifically, we design new Gibbs state preparation methods that do not rely on simulating Lindbladian evolution, thus avoiding the overhead from it. For local Lindbladians consisting of $M$ terms, this approach reduces the cost by a factor of $O(M)$. We also combine the detectability lemma operator and quantum singular value transformation to implement ground state projection operators of frustration-free Hamiltonians, resulting in a quadratic speedup in the spectral gap dependence. Applying this method to Lindbladians for the Gibbs state of local commuting Hamiltonians, we achieve quadratically better dependence on the Lindbladian spectral gap.
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