We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over the Chebyshev approximation of the target function while keeping the matrix oracle quantum, and is assisted by a variant of the Hadamard test that removes the need for post-selection. The resulting statistical overhead is similar to the fully quantum case and does not incur any circuit depth degradation. On the contrary, the average circuit depth is shown to get smaller, yielding equivalent reductions in noise sensitivity, as explicitly shown for depolarizing noise and coherent errors. We apply our technique to partition-function estimation, linear system solvers, and ground-state energy estimation. For these cases, we prove advantages on average depths, including quadratic speed-ups on costly parameters and even the removal of the approximation-error dependence.

我们提出了一种混合量子经典框架，用于模拟比标准量子奇异值变换更适合早期容错量子硬件的通用矩阵函数。该方法基于目标函数的切比雪夫近似的随机化，同时保持矩阵预言量子，并由哈达玛测试的变体辅助，消除了后选择的需要。由此产生的统计开销与完全量子情况类似，并且不会导致任何电路深度退化。相反，平均电路深度变得更小，导致噪声灵敏度等效降低，如去极化噪声和相干误差明确所示。我们将我们的技术应用于配分函数估计、线性系统求解器和基态能量估计。对于这些情况，我们证明了平均深度的优势，包括昂贵参数的二次加速，甚至消除了近似误差依赖性。