Variational quantum state diagonalization
Variational quantum state diagonalization
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DOI：
10.1038/s41534-019-0167-6
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发表时间：
2019-06-26
影响因子：
7.6
通讯作者：
Coles, Patrick J.
中科院分区：
文献类型：
--
作者：
LaRose, Ryan;Tikku, Arkin;Coles, Patrick J.
变分混合量子经典算法是近期在量子计算机上实现的有希望的候选者。在这些算法中，量子计算机评估门序列的成本（与经典成本评估相比具有加速），并且经典计算机使用此信息来调整门序列的参数。在这里，我们提出了这样一个量子态对角化的算法。状态对角化在凝聚态物理学中有应用（例如，纠缠光谱学）以及机器学习（例如，主成分分析）。对于量子态ρ与门序列U，我们的成本函数量化了U ρ U-匕首距离对角线有多远。我们引入短深度量子电路来量化我们的成本。最小化该成本返回近似对角化ρ的门序列。然后可以读出ρ的最大特征值和相关特征向量的近似值。作为一个证明的原则，我们实现了我们的算法Rigetti的量子计算机对角化一个量子比特状态和模拟器上找到海森堡模型基态的纠缠谱。
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state rho and gate sequence U, our cost function quantifies how far U rho U-dagger is from being diagonal. We introduce short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes rho. One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of rho. As a proof-of-principle, we implement our algorithm on Rigetti's quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.