论文标题
阻止经典数据矩阵所需的量子资源
Quantum Resources Required to Block-Encode a Matrix of Classical Data
论文作者
论文摘要
我们为几种块编码密集的$ n \ times n $ n $矩阵提供了模块化电路级实现和资源估算，以限定精度$ε$；最小的深度方法达到了$ \ Mathcal {o} {（\ log（n/ε））}的$ t $ -Depth，而最小计数方法实现了$ \ nathcal {o} $ t $ count，我们研究了不同方法之间的资源权衡，并探讨了两个单独的量子随机访问存储器（QRAM）的实现。作为本分析的一部分，我们提供了一种新颖的状态准备程序，其中$ t $ -Depth $ \ Mathcal {o} {（\ log（n/ε））} $，通过缩放$ \ Mathcal {o} {O} {（\ log log^2（n/ε））} $改进了先前的构造。我们的结果超出了简单的查询复杂性，并在假定量子算法可以访问大量经典数据时，为资源成本提供了清晰的图像。
We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense $N\times N$ matrix of classical data to precision $ε$; the minimal-depth method achieves a $T$-depth of $\mathcal{O}{(\log (N/ε))},$ while the minimal-count method achieves a $T$-count of $\mathcal{O}{(N\log(1/ε))}$. We examine resource tradeoffs between the different approaches, and we explore implementations of two separate models of quantum random access memory (QRAM). As part of this analysis, we provide a novel state preparation routine with $T$-depth $\mathcal{O}{(\log (N/ε))}$, improving on previous constructions with scaling $\mathcal{O}{(\log^2 (N/ε))}$. Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.
