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arXiv 2108.04258quant-ph
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量子动力学的量子算法:自旋玻色子模型的性能研究

Quantum algorithms for quantum dynamics: A performance study on the spin-boson model

Alexander Miessen, Pauline J. Ollitrault, Ivano Tavernelli

摘要:

用于量子动力学模拟的量子算法传统上基于实现时间演化算子的Trotter近似。这种方法通常依赖于深层电路,因此受到可用噪声和近期量子硬件的实质性限制的阻碍。另一方面,变分量子算法已成为不可或缺的替代方案,可以在当今的硬件上进行小规模模拟。然而,尽管最近发展的变分量子算法的量子动力学,其效率和可扩展性的详细评估尚未提出。为了填补这一空白,我们采用了基于麦克拉克伦原理的变分量子算法来模拟自旋玻色子模型的动态变化水平的现实硬件噪声以及在不同的物理制度,并讨论了算法的准确性和缩放行为作为系统大小的函数。我们观察到一个很好的性能的变分方法结合使用的一般,物理动机的波函数ananterior,并将其与传统的一阶Trotter演化。最后,在此基础上,我们对一个经典难处理系统的模拟进行了标度预测。我们表明,尽管提供了一个明确的减少量子门的成本,变分方法在其目前的实施是不可能导致一个量子优势的时间依赖性问题的解决方案。

英文摘要:

Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial limitations of available noisy and near-term quantum hardware. On the other hand, variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. However, despite the recent development of variational quantum algorithms for quantum dynamics, a detailed assessment of their efficiency and scalability is yet to be presented. To fill this gap, we applied a variational quantum algorithm based on McLachlan's principle to simulate the dynamics of a spin-boson model subject to varying levels of realistic hardware noise as well as in different physical regimes, and discuss the algorithm's accuracy and scaling behavior as a function of system size. We observe a good performance of the variational approach used in combination with a general, physically motivated wavefunction ansatz, and compare it to the conventional first-order Trotter-evolution. Finally, based on this, we make scaling predictions for the simulation of a classically intractable system. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage for the solution of time-dependent problems.

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