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arXiv 1906.09253quant-ph
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变分量子保真度估计

Variational Quantum Fidelity Estimation

M. Cerezo, Alexander Poremba, Lukasz Cincio, Patrick J. Coles

备注：
6 + 8 pages, 4 figures
发表信息：
Quantum 4, 248 (2020)
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摘要：

计算量子态保真度对于验证和表征量子计算机上制备的态具有重要意义。在这项工作中，我们提出了新的下限和上限的保真度$F(ρ,σ)$的基础上的“截断保真度”$F(ρ_m, σ)$，这是评估状态$ρ_m$通过投影$ρ$到其$m$ -最大特征值。我们的边界可以细化，即，它们与$m$单调收紧。为了计算我们的边界，我们引入了一个混合量子经典算法，称为变分量子保真度估计，它包括三个步骤：（1）变分对角化$ρ$，（2）计算矩阵元素的$σ$的特征基的$ρ$，和（3）结合这些矩阵元素来计算我们的边界。我们的算法是针对的情况下，$σ$是任意的和$ρ$是低秩，我们称之为低秩保真度估计，我们证明了一个经典的算法不能有效地解决这个问题。最后，我们证明了我们的边界可以检测量子相变，往往比以前已知的可计算的现实情况下的边界更紧。

英文摘要：

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(ρ,σ)$ based on the "truncated fidelity" $F(ρ_m, σ)$, which is evaluated for a state $ρ_m$ obtained by projecting $ρ$ onto its $m$-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with $m$. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize $ρ$, (2) compute matrix elements of $σ$ in the eigenbasis of $ρ$, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where $σ$ is arbitrary and $ρ$ is low rank, which we call low-rank fidelity estimation, and we prove that a classical algorithm cannot efficiently solve this problem. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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