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Optimal compression of constrained quantum time evolution
Physical Review B ( IF 3.7 ) Pub Date : 2024-05-15 , DOI: 10.1103/physrevb.109.205134
Maurits S. J. Tepaske 1 , David J. Luitz 1 , Dominik Hahn 2
Affiliation  

The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The minimization of the circuit depth for a given quantum algorithm is therefore highly desirable, since shallow circuits generally are less vulnerable to decoherence. Recently, it was shown that variational circuits are a promising approach to outperform current state-of-the-art methods such as Trotter decomposition, although the optimal choice of parameters is a computationally demanding task. In this work, we demonstrate a simplification of the variational optimization of circuits implementing the time evolution operator of local Hamiltonians by directly encoding constraints of the physical system under consideration. We study the expressibility of such constrained variational circuits for different models and constraints. Our results show that the encoding of constraints allows a reduction of optimization cost by more than one order of magnitude and scalability to arbitrary large system sizes, without loosing accuracy in most systems. Furthermore, we discuss the exceptions in locally constrained systems and provide an explanation by means of an restricted lightcone width after incorporating the constraints into the circuits.

中文翻译:

约束量子时间演化的最优压缩

量子多体系统的时间演化是近期量子计算机最有前途的应用之一。然而,当前量子设备的实用性受到硬件错误激增的严重阻碍。因此,对于给定的量子算法,电路深度的最小化是非常理想的,因为浅电路通常不易受到退相干的影响。最近,研究表明,变分电路是一种有前途的方法,其性能优于 Trotter 分解等当前最先进的方法,尽管参数的最佳选择是一项计算要求较高的任务。在这项工作中,我们展示了通过直接编码所考虑的物理系统的约束来实现局部哈密顿量的时间演化算子的​​电路变分优化的简化。我们研究了这种受约束变分电路对于不同模型和约束的可表达性。我们的结果表明,约束编码可以将优化成本降低一个数量级以上,并且可以扩展到任意大型系统规模,而不会损失大多数系统的准确性。此外,我们讨论了局部约束系统中的例外情况,并在将约束纳入电路后通过受限的光锥宽度提供了解释。
更新日期:2024-05-15
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