Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Abstract
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.
Featured image: A sketch of the p-VQD algorithm.
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Cited by
[1] Yong-Xin Yao, Niladri Gomes, Feng Zhang, Cai-Zhuang Wang, Kai-Ming Ho, Thomas Iadecola, and Peter P. Orth, “Adaptive Variational Quantum Dynamics Simulations”, PRX Quantum 2 3, 030307 (2021).
[2] Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, and Kishor Bharti, “NISQ Algorithm for Hamiltonian Simulation via Truncated Taylor Series”, arXiv:2103.05500.
[3] Michael R. Geller, Zoë Holmes, Patrick J. Coles, and Andrew Sornborger, “Experimental Quantum Learning of a Spectral Decomposition”, arXiv:2104.03295.
[4] Kian Hwee Lim, Tobias Haug, Leong Chuan Kwek, and Kishor Bharti, “Fast-Forwarding with NISQ Processors without Feedback Loop”, arXiv:2104.01931.
[5] Tobias Haug and M. S. Kim, “Optimal training of variational quantum algorithms without barren plateaus”, arXiv:2104.14543.
[6] Julien Gacon, Christa Zoufal, Giuseppe Carleo, and Stefan Woerner, “Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information”, arXiv:2103.09232.
[7] Yongdan Yang, Bing-Nan Lu, and Ying Li, “Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer”, arXiv:2106.09880.
[8] Paolo P. Mazza, Dominik Zietlow, Federico Carollo, Sabine Andergassen, Georg Martius, and Igor Lesanovsky, “Machine learning time-local generators of open quantum dynamics”, Physical Review Research 3 2, 023084 (2021).
[9] Refik Mansuroglu, Samuel Wilkinson, Ludwig Nützel, and Michael J. Hartmann, “Classical Variational Optimization of Gate Sequences for Time Evolution of Large Quantum Systems”, arXiv:2106.03680.
[10] Michael R. Geller, Andrew Arrasmith, Zoë Holmes, Bin Yan, Patrick J. Coles, and Andrew Sornborger, “Quantum simulation of operator spreading in the chaotic Ising model”, arXiv:2106.16170.
[11] Lucas Slattery, Benjamin Villalonga, and Bryan K. Clark, “Unitary Block Optimization for Variational Quantum Algorithms”, arXiv:2102.08403.
[12] Rouven Koch and Jose L. Lado, “Neural network enhanced hybrid quantum many-body dynamical distributions”, arXiv:2105.03129.
[13] Kishor Bharti, Tobias Haug, Vlatko Vedral, and Leong-Chuan Kwek, “NISQ Algorithm for Semidefinite Programming”, arXiv:2106.03891.
The above citations are from SAO/NASA ADS (last updated successfully 2021-07-28 10:06:09). The list may be incomplete as not all publishers provide suitable and complete citation data.
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