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arXiv 2102.04313quant-phcs.LGstat.ML
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在量子硬件上进行高保真的长时间模拟

Long-time simulations with high fidelity on quantum hardware

Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室);University of Oxford(牛津大学);University of Connecticut(康涅狄格大学)

Joe Gibbs, Kaitlin Gili, Zoë Holmes, Benjamin Commeau, Andrew Arrasmith, Lukasz Cincio, Patrick J. Coles, Andrew Sornborger

摘要:

中等大小的量子计算机现在可以通过云公开访问,这为量子系统的动态模拟提供了令人兴奋的可能性。然而,虽然这些设备快速改进,但相干时间短,限制了可能成功实现的算法的深度。在这里,我们证明,尽管有这些限制,它是可以实现长时间,高保真度的模拟当前的硬件。具体来说,我们在Rigetti和IBM量子计算机上模拟XY模型的自旋链,在超过600个时间步长内保持至少0.9的保真度。这比使用迭代Trotter方法可能的时间长150倍。我们的模拟使用一种新的算法,我们称之为固定状态变分快速转发(fsVFF)算法。该算法通过寻找短时演化幺正的近似对角化,减小了量子模拟所需的电路深度和宽度。至关重要的是,fsVFF只需要在初始状态所跨越的子空间上找到对角化,而不是像以前的方法那样在整个希尔伯特空间上,从而大大减少了所需的资源。我们进一步证明了fsVFF的可行性,通过大数值实现的算法,以及分析其噪声弹性和模拟误差的缩放。

英文摘要:

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented. Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps. This is a factor of 150 longer than is possible using the iterated Trotter method. Our simulations are performed using a new algorithm that we call the fixed state Variational Fast Forwarding (fsVFF) algorithm. This algorithm decreases the circuit depth and width required for a quantum simulation by finding an approximate diagonalization of a short time evolution unitary. Crucially, fsVFF only requires finding a diagonalization on the subspace spanned by the initial state, rather than on the total Hilbert space as with previous methods, substantially reducing the required resources. We further demonstrate the viability of fsVFF through large numerical implementations of the algorithm, as well as an analysis of its noise resilience and the scaling of simulation errors.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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