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An efficient quantum algorithm for the time evolution of parameterized circuits
Quantum ( IF 6.4 ) Pub Date : 2021-07-28 , DOI: 10.22331/q-2021-07-28-512
Stefano Barison 1 , Filippo Vicentini 1 , Giuseppe Carleo 1
Affiliation  

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

中文翻译:

一种用于参数化电路时间演化的高效量子算法

我们引入了一种新颖的混合算法,以使用参数化量子电路来模拟量子系统的实时演化。该方法名为“投影-变分量子动力学”(p-VQD),实现了精确时间演化到参数化流形的迭代全局投影。在小时间步长限制下,这等价于麦克拉克兰变分原理。我们的方法是有效的,因为它展示了具有变分参数总数的最佳线性缩放。此外,它是全局的,因为它使用变分原理一次优化所有参数。我们方法的全局性显着扩展了现有有效变分方法的范围,相反,它通常依赖于变分参数的受限子集的迭代优化。通过数值实验,我们还表明,我们的方法特别优于现有的基于时间相关变分原理的全局优化算法,由于需要对参数数进行二次缩放,因此不适用于大型参数化量子电路。
更新日期:2021-09-06
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