论文标题
费米文断层扫描和学习
Fermionic tomography and learning
论文作者
论文摘要
通过经典阴影的影子断层扫描是一种估计量子状态特性的最新方法。我们基于既是费米子高斯和克利福德的统一的集合，又提供了对这种方法的最近提出的实例化的简化，组合分析。使用此分析，我们得出了估计器方差的校正表达式。然后，我们展示这是如何通过纯净的费米斯高斯状态（可证明）和形式的$ x $类似运算符（$ | \ Mathbf 0 \ rangle \ langle \langleψ| $ + h.c。）的忠诚度有效的估计协议（通过数字证据）。我们还构建了较小的测量库集合，从而产生完全相同的量子通道，这可能有助于汇编。我们使用这些工具来表明，可以将$ n $ - electron，$ m $ - mode slater决定因素在$ε$ fidelity之内学习给给定$ o（n^2 m^7 \ log（m /δ） /ε^2）slater确定剂的样本。
Shadow tomography via classical shadows is a state-of-the-art approach for estimating properties of a quantum state. We present a simplified, combinatorial analysis of a recently proposed instantiation of this approach based on the ensemble of unitaries that are both fermionic Gaussian and Clifford. Using this analysis, we derive a corrected expression for the variance of the estimator. We then show how this leads to efficient estimation protocols for the fidelity with a pure fermionic Gaussian state (provably) and for an $X$-like operator of the form ($|\mathbf 0\rangle\langleψ|$ + h.c.) (via numerical evidence). We also construct much smaller ensembles of measurement bases that yield the exact same quantum channel, which may help with compilation. We use these tools to show that an $n$-electron, $m$-mode Slater determinant can be learned to within $ε$ fidelity given $O(n^2 m^7 \log(m / δ) / ε^2)$ samples of the Slater determinant.
