Variational microcanonical estimator
Variational microcanonical estimator
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DOI：
10.1103/physrevresearch.5.033224
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发表时间：
2023-01
影响因子：
4.2
通讯作者：
Kl'ee Pollock;P. P. Orth-P.;Thomas Iadecola
中科院分区：
文献类型：
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作者：
Kl'ee Pollock;P. P. Orth-P.;Thomas Iadecola
我们提出了一个变分量子算法估计模型中的微正则期望值服从本征态热化假设。使用一个放松的标准收敛的变分优化循环，该算法产生弱纠缠叠加的本征态在一个给定的目标能量密度。这些变分状态的合奏，然后用来估计微正则平均的本地运营商，与错误的主要贡献减少最初作为一个幂律的合奏的大小，并最终限制了一个小的偏差。我们将该算法应用到一维混合场伊辛模型，它收敛的深度大致线性的系统大小的ananterior电路。最准确的热估计是为中等能量密度而产生的。在我们的误差分析中，我们发现与最近的作品调查的本征态热化假设的基础连接。特别是，当地运营商的能量基础矩阵元素的失败表现为\textit{独立}随机变量是一个潜在的错误源，该算法可以克服平均在一个合奏的变分状态。
We propose a variational quantum algorithm for estimating microcanonical expectation values in models obeying the eigenstate thermalization hypothesis. Using a relaxed criterion for convergence of the variational optimization loop, the algorithm generates weakly entangled superpositions of eigenstates at a given target energy density. An ensemble of these variational states is then used to estimate microcanonical averages of local operators, with an error whose dominant contribution decreases initially as a power law in the size of the ensemble and is ultimately limited by a small bias. We apply the algorithm to the one-dimensional mixed-field Ising model, where it converges for ansatz circuits of depth roughly linear in system size. The most accurate thermal estimates are produced for intermediate energy densities. In our error analysis, we find connections with recent works investigating the underpinnings of the eigenstate thermalization hypothesis. In particular, the failure of energy-basis matrix elements of local operators to behave as \textit{independent} random variables is a potential source of error that the algorithm can overcome by averaging over an ensemble of variational states.