标题： 压缩酉算子和经典阴影层析技术 显示英文标题

标题： Contractive Unitary and Classical Shadow Tomography

摘要： 量子技术的快速发展要求对复杂的量子多体态进行有效的表征。 然而，完整的量子态层析成像需要随着系统尺寸的指数增长而增加测量次数，这阻碍了其在大规模量子设备中的实际应用。 在此方向上的一个重大最近突破称为经典阴影层析成像，通过在测量前实施随机 Clifford 旋转，显著降低了样本复杂度，即估计状态属性所需的样本数量。 尽管有诸多近期努力，但对于提取任何非连续局部算符，当其大小为$\sim \mathbf{k}$时，将样本复杂度降低到$\mathbf{2^k}$以下仍然是一个挑战。 在本工作中，我们使用一种混合局部随机和全局确定性幺正操作的协议，实现了显著更小的样本复杂度$\mathbf{\sim 1.8^k}$。 关键见解是发现了一种确定性的全局幺正操作，称为\textit{压缩单位算子}，它在减少算符大小以提高层析成像效率方面更为高效。 该收缩性幺正操作完美地结合了原子阵列量子计算平台的优势，并可在原子阵列量子处理器中轻松实现。 更重要的是，它在经典阴影层析成像中提出了一种新的策略，表明随机-确定性混合协议可以比完全随机测量更高效。 显示英文摘要

摘要： The rapid development of quantum technology demands efficient characterization of complex quantum many-body states. However, full quantum state tomography requires an exponential number of measurements in system size, preventing its practical use in large-scale quantum devices. A major recent breakthrough in this direction, called classical shadow tomography, significantly reduces the sample complexity, the number of samples needed to estimate properties of a state, by implementing random Clifford rotations before measurements. Despite many recent efforts, reducing the sample complexity below $\mathbf{2^k}$ for extracting any non-successive local operators with a size $\sim \mathbf{k}$ remains a challenge. In this work, we achieve a significantly smaller sample complexity of $\mathbf{\sim 1.8^k}$ using a protocol that hybridizes locally random and globally deterministic unitary operations. The key insight is the discovery of a deterministic global unitary, termed as \textit{contractive unitary}, which is more efficient in reducing the operator size to enhance tomography efficiency. The contractive unitary perfectly matches the advantages of the atom array quantum computation platform and is readily realized in the atom array quantum processor. More importantly, it highlights a new strategy in classical shadow tomography, demonstrating that a random-deterministic hybridized protocol can be more efficient than fully random measurements.