论文标题
恒定量子深度的多变量痕量估计
Multivariate trace estimation in constant quantum depth
论文作者
论文摘要
人们认为，需要一个深度-U $θ（m）$量子电路来估计$ m $密度矩阵的产物（即多变量痕迹）的痕迹，这对于在凝结物质和量子信息科学中的应用中的次级列表至关重要。我们通过为任务构造恒定的量子深度电路，这证明了这种信念过于保守，灵感来自于Shor误差校正方法。此外，我们的电路仅在二维电路中需要本地门 - 我们展示了如何以高度平行的方式在类似于Google的Sycamore处理器的体系结构上实现它。借助这些功能，我们的算法带来了更接近近期量子处理器功能的多元痕量估计的核心任务。我们使用定理实例化后一种应用，以估计具有“良好行为”多项式近似值的量子状态的非线性函数。
There is a folkloric belief that a depth-$Θ(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science. We prove that this belief is overly conservative by constructing a constant quantum-depth circuit for the task, inspired by the method of Shor error correction. Furthermore, our circuit demands only local gates in a two dimensional circuit -- we show how to implement it in a highly parallelized way on an architecture similar to that of Google's Sycamore processor. With these features, our algorithm brings the central task of multivariate trace estimation closer to the capabilities of near-term quantum processors. We instantiate the latter application with a theorem on estimating nonlinear functions of quantum states with "well-behaved" polynomial approximations.
