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arXiv 2012.09238quant-ph
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Hubbard模型的早期容错模拟

Early fault-tolerant simulations of the Hubbard model

Earl T. Campbell

备注：
Some typos corrected since V1 with gate counts slightly adjusted. V2 more polished. V4 small typoes fixed (see App E) with thanks to Sam McArdle and Mark Steudtner for detailed questions on this section
发表信息：
Quantum Sci. Technol. 7 015007 (2021)
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AI总结：

本文提出一种新的解析方法优化了Hubbard模型早期容错模拟的误差界限，并引入适用于任意尺寸晶格的plaquette Trotterization技术，在相位估计任务中显著降低了非Clifford门数量。

摘要：

Hubbard模型的模拟是容错量子计算机首个实用应用的首要候选者。最近一项关于Hubbard模型早期模拟的量子算法研究[Kivlichan et al. Quantum 4 296 (2019)]发现，在长度为L=2^k的L×L晶格上，结合快速费米子傅里叶变换（FFFT）的split-operator Trotterization实现了最低的资源成本。在长度L≠2^k的晶格上，可以使用Givens旋转代替FFFT，但会导致更高的资源成本。我们提出了一种新的解析方法来限制由Trotterization引起的模拟误差，该方法为split-operator FFFT方法提供了更紧的界限，使误差界限提高了16倍。此外，我们引入了适用于任意尺寸晶格的plaquette Trotterization，并应用我们改进的误差界限分析来展示其具有竞争力的资源成本。我们考虑了一个相位估计任务，并表明在8×8和16×16晶格上，plaquette Trotterization将非Clifford门的数量减少了5.5倍至9倍（取决于参数区间），而对于其他非L=2^k形式的晶格尺寸，减少的幅度更大。总之，我们发现使用约一百万个Toffoli门的容错量子计算机具有潜在的实用应用。

英文摘要：

Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.} Quantum 4 296 (2019)] found that the lowest resource costs were achieved by split-operator Trotterization combined with the fast-fermionic Fourier transform (FFFT) on an $L \times L$ lattice with length $L=2^k$. On lattices with length $L \neq 2^k$, Givens rotations can be used instead of the FFFT but lead to considerably higher resource costs. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the split-operator FFFT method, leading to $16 \times$ improvement in error bounds. Furthermore, we introduce plaquette Trotterization that works on any size lattice and apply our improved error bound analysis to show competitive resource costs. We consider a phase estimation task and show plaquette Trotterization reduces the number of non-Clifford gates by a factor $5.5\times$ to $9 \times$ (depending on the parameter regime) over the best previous estimates for $8 \times 8$ and $16 \times 16$ lattices and a much larger factor for other lattice sizes not of the form $L=2^k$. In conclusion, we find there is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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