Adaptive variational quantum eigensolvers for highly excited states
Adaptive variational quantum eigensolvers for highly excited states
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DOI：
10.1103/physrevb.104.075159
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发表时间：
2021-04
影响因子：
3.7
通讯作者：
Feng Zhang;N. Gomes;Yongxin Yao;P. P. Orth-P.;Thomas Iadecola
中科院分区：
文献类型：
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作者：
Feng Zhang;N. Gomes;Yongxin Yao;P. P. Orth-P.;Thomas Iadecola
量子多体系统的高激发态是量子动力学和热化研究的中心对象，由于其体积定律纠缠内容而对经典计算方法提出了挑战。在这项工作中，我们探索了变分量子算法近似此类状态的潜力。我们提出了一种自适应变分算法，即自适应 VQE-X，它通过尝试最小化相对于 $H$ 的能量方差，为多体哈密顿量 $H$ 的任意本征态自行生成变分拟态。我们通过将其应用于具有可积和不可积状态的伊辛自旋链来对该方法进行基准测试，其中我们计算各种感兴趣的量，包括总能量、磁化密度和纠缠熵。我们还将自适应 VQE-X 的性能与折叠谱方法的自适应变体进行了比较。对于这两种方法，我们发现算法的性能很大程度上取决于用于自适应构造 ansatz 的算子池的选择。特别是，包括远程双体门的算子池加速了两种算法在不可积状态下的收敛。我们还研究了变分参数的数量随系统尺寸的变化，发现可能需要指数级数量的参数来近似各个高度激发态。尽管如此，我们认为这些方法为使用量子算法研究多体系统的有限能量密度特性奠定了基础。
Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$ by attempting to minimize the energy variance with respect to $H$. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. We also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems.