AI 中文总结
本研究提出量子算法在ADK弦论景观玩具模型中寻找小宇宙学常数真空，利用线性结构将问题简化为碰撞问题，实现查询复杂度从$2^{N/2}$降至$2^{N/3}$，大幅降低计算成本。
AI 中文摘要
我们研究了在Arkani-Hamed、Dimopoulos和Kachru提出的弦论景观玩具模型中，寻找具有小宇宙学常数的真空态的量子算法。首先，我们构造了一个函数值预言机，并将其用于Grover搜索，查询复杂度为$\mathcal{O}(2^{N/2})$，其中$N$是标量场的数量。然后，我们指出，通过利用真空能量的线性特性，该问题可以简化为比特串两个区块之间的碰撞问题。利用这一结构，我们构造了两个查询复杂度为$\mathcal{O}(2^{N/3})$的量子算法。与Denef和Douglas的伪多项式经典算法相比，对于物理上合理的参数值，量子算法在计算成本上实现了大幅降低。
英文摘要
We study quantum algorithms for finding a vacuum with a small cosmological constant in the toy model for string Landscape proposed by Arkani-Hamed, Dimopoulos, and Kachru. First, we construct a function-value oracle and use it for Grover search with query complexity $\mathcal{O}(2^{N/2})$, where $N$ is the number of scalar fields. Then, we point out that, by exploiting the linearity of the vacuum energy, the problem can be reduced to a collision problem between two blocks of the bit string. With this structure, we construct two quantum algorithms with query complexity $\mathcal{O}(2^{N/3})$. Compared with the pseudo-polynomial classical algorithm of Denef and Douglas, the quantum algorithms yield a large reduction in computational cost for the physically motivated parameter values.
Comments18 pages, 6 figures
