论文标题
甚至较短的量子电路，用于对早期耐故障量子计算机进行相位估算的较短电路
Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
论文作者
论文摘要
我们开发具有具有独特功能的相位估计方法：其最大运行时（确定电路深度）为$δ/ε$，其中$ε$是目标精度，并且预恒定$δ$可以任意接近$ 0 $，因为初始状态接近目标特征。该算法的总成本满足了Heisenberg限制缩放$ \ widetilde {\ Mathcal {o}}（ε^{ - 1}）$。结果，我们的算法可能会显着降低对早期易于断层量子计算机执行相位估计任务的电路深度。关键技术是一种简单的子例程，称为量子复合体指数最小二乘（qcels）。当初始状态和基态之间的重叠时，我们的算法可以很容易地用于减小电路深度以估计量子量的量子能量。如果此初始重叠很小，我们可以将我们的方法与[Lin，Tong，Prx Quantum 3，010318，2022]中开发的傅立叶滤波方法相结合，而所得算法可在存在大型相对重叠的情况下降低电路深度。相对重叠条件类似于光谱差距假设，但它知道初始状态的信息，因此适用于某些光谱差距较小的汉密尔顿人。我们观察到，在各种设置下的数值实验中，可以将电路深度降低两个数量级。
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $δ/ε$, where $ε$ is the target precision, and the preconstant $δ$ can be arbitrarily close to $0$ as the initial state approaches the target eigenstate. The total cost of the algorithm satisfies the Heisenberg-limited scaling $\widetilde{\mathcal{O}}(ε^{-1})$. As a result, our algorithm may significantly reduce the circuit depth for performing phase estimation tasks on early fault-tolerant quantum computers. The key technique is a simple subroutine called quantum complex exponential least squares (QCELS). Our algorithm can be readily applied to reduce the circuit depth for estimating the ground-state energy of a quantum Hamiltonian, when the overlap between the initial state and the ground state is large. If this initial overlap is small, we can combine our method with the Fourier filtering method developed in [Lin, Tong, PRX Quantum 3, 010318, 2022], and the resulting algorithm provably reduces the circuit depth in the presence of a large relative overlap compared to $ε$. The relative overlap condition is similar to a spectral gap assumption, but it is aware of the information in the initial state and is therefore applicable to certain Hamiltonians with small spectral gaps. We observe that the circuit depth can be reduced by around two orders of magnitude in numerical experiments under various settings.
