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A diagrammatic approach to variational quantum ansatz construction
Quantum ( IF 5.1 ) Pub Date : 2021-12-02 , DOI: 10.22331/q-2021-12-02-596
Y. Herasymenko 1 , T.E. O'Brien 1
Affiliation  

Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.

中文翻译:

变分量子 ansatz 构造的图解方法

变分量子本征求解器 (VQE) 是一类很有前途的量子算法,用于在近期量子器件中准备近似基态。最小化这种近似中的误差需要使用针对所研究系统的物理考虑来设计 ansatze。其中一个考虑因素是尺寸扩展性,这意味着基态量子相关性将在 ansatz 中紧凑地表示。然而,在数字量子计算机上,尺寸广泛的 ansatzes 通常需要通过 Trotter-Suzuki 方法进行扩展。这些会给近似值带来额外的成本和误差。在这项工作中,我们提出了一个数字 VQE ansatzes 的图解方案,它是规模广泛但不依赖于 Trotterization。我们首先设计了一系列数字 ansatze,它们以最少的自由参数探索整个 Hilbert 空间。然后,我们演示了如何通过强制执行目标系统的对称约束,或通过将它们用作父级 ansatze 来压缩任意数字 ansatze,以实现越来越长但越来越准确的 sub-ansatze 层次结构。我们应用微扰分析并开发图解形式,以确保生成的层次结构的大小扩展性。我们在短自旋链上测试我们的方法,在横向场 Ising 模型的顺磁和铁磁相中找到了对基态的良好收敛。或者通过将它们用作父级 ansatzes 来获得越来越长但越来越准确的 sub-ansatzes 层次结构。我们应用微扰分析并开发图解形式,以确保生成的层次结构的大小扩展性。我们在短自旋链上测试我们的方法,在横向场 Ising 模型的顺磁和铁磁相中找到了对基态的良好收敛。或者通过将它们用作父级 ansatzes 来获得越来越长但越来越准确的 sub-ansatzes 层次结构。我们应用微扰分析并开发图解形式,以确保生成的层次结构的大小扩展性。我们在短自旋链上测试我们的方法,在横向场 Ising 模型的顺磁和铁磁相中找到了对基态的良好收敛。
更新日期:2021-12-02
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