论文标题
费尔米金部分层析成像通过古典阴影
Fermionic partial tomography via classical shadows
论文作者
论文摘要
我们提出了一项层压协议，用于估计$ n $ mode fermionic状态的任何$ k $降低密度矩阵（$ k $ -rdm），这是近期量子算法的无处不在的一步，用于模拟多体物理，化学，化学，化学，化学和材料。我们的方法将经典阴影的框架扩展到了fermionic设置的一种随机方法，用于学习量子状态属性的集合。我们的采样协议使用由一组Fermionic Gaussian Unitaries产生的随机测量设置，可通过线性深度电路实现。我们证明，将所有$ k $ -rdm元素估算为加法精度$ \ varepsilon $按$ \ binom {n} {k} {k} k^{3/2} \ log（n） / \ varepsilon^2 $重复的状态准备，这是最佳的，这是最佳的，这是最佳的。此外，与先前的确定性策略相比，数值计算表明，我们的协议在$ k \ geq 2 $的恒定间接费用方面有了很大的改善。我们还将方法调整为粒子对称性，其中额外的电路深度可能以大约2-5倍重复的成本减半。
We propose a tomographic protocol for estimating any $ k $-body reduced density matrix ($ k $-RDM) of an $ n $-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits. We prove that estimating all $ k $-RDM elements to additive precision $ \varepsilon $ requires on the order of $ \binom{n}{k} k^{3/2} \log(n) / \varepsilon^2 $ repeated state preparations, which is optimal up to the logarithmic factor. Furthermore, numerical calculations show that our protocol offers a substantial improvement in constant overheads for $ k \geq 2 $, as compared to prior deterministic strategies. We also adapt our method to particle-number symmetry, wherein the additional circuit depth may be halved at the cost of roughly 2-5 times more repetitions.
