AI 中文总结
该研究提出一类无需辅助量子比特与受控Grover操作、深度和重复次数可调的幅度估计算法，在全参数区间实现近最优查询-深度权衡，边界处仍保持量子加速，实验验证其精度高、开销低，适用于早期容错量子计算的多种场景。
AI 中文摘要
我们提出了一类电路深度$M$和电路重复次数$N$可调的幅度估计算法，该算法既不需要辅助量子比特，也不需要受控Grover操作。对于Grover角的加性误差$ε$，这类算法在$λ∈[0,π/2]$的全区间内一致实现了近最优的查询-深度权衡关系$M^2N∈\widetilde{O}(ε^{-2})$，覆盖了从$M=1$时的经典采样到$M=Θ(ε^{-1})$时的海森堡极限的全部范围。此前的深度可调相关工作仅在远离$λ→0$或$π/2$的边界处，或是在离散的深度权衡点上才能给出相当的角度精度保证，而我们的保证可扩展至两个边界，因此量子加速在边界处依然存在，不会退化到经典采样水平。数值实验证实了预测的一致角度精度，且实际开销较低，这类算法是早期容错阶段实用幅度估计的有力候选方案，可应用于重叠认证、试验态验证和蒙特卡洛方法等场景。
英文摘要
We develop a class of amplitude estimation algorithms with tunable circuit depth $M$ and circuit repetitions $N$, requiring neither ancilla qubits nor controlled Grover operations. For additive error $ε$ in the Grover angle, they attain the nearly optimal query-depth tradeoff $M^2N\in\widetilde{O}(ε^{-2})$ uniformly over $λ\in[0,π/2]$, spanning the full range from classical sampling at $M=1$ to the Heisenberg limit at $M=Θ(ε^{-1})$. While prior depth-tunable work establishes comparable angle-accuracy guarantees only away from the boundaries $λ\to0$ or $π/2$ or at discrete depth tradeoffs, our guarantee extends to both boundaries, so the quantum speedup persists there rather than degrading to classical sampling. Numerical experiments confirm the predicted uniform angle accuracy and show low overhead in practice, making them strong candidates for practical amplitude estimation in the early fault-tolerant regime, with applications such as overlap certification, trial-state verification, and Monte Carlo methods.
Comments20 pages, 2 figures
