论文标题
变分量子状态层
Variational Quantum State Eigensolver
论文作者
论文摘要
提取指数型矩阵的特征值和特征向量将是近期量子计算机的重要应用。当矩阵是哈密顿量时，变异量子本素层（VQE）治疗了案例。在这里，我们解决矩阵是密度矩阵$ρ$的情况。我们介绍了变异量子状态元素（VQSE），它类似于VQE，因为它在变化上学习了$ρ$的最大特征值以及准备相应的特征vectors的门序$ v $。 VQSE利用对角和多数化之间的连接来定义成本函数$ c = \ tr（\tildeρh）$，其中$ h $是非降级的哈密顿量。由于Schur-Concavity，$ c $当$ \tildeρ=vρv^\匕首$在$ h $的特征性的对角线上最小化。 VQSE仅需要通过VQSE算法的$ρ$（仅$ n $ Qubits）的单个副本，这使其适合近期实施。我们启发了VQSE的两个应用：（1）主成分分析和（2）误差缓解。
Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix $ρ$. We introduce the Variational Quantum State Eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of $ρ$ as well as a gate sequence $V$ that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function $C=\Tr(\tildeρ H)$ where $H$ is a non-degenerate Hamiltonian. Due to Schur-concavity, $C$ is minimized when $\tildeρ = VρV^\dagger$ is diagonal in the eigenbasis of $H$. VQSE only requires a single copy of $ρ$ (only $n$ qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.
