1Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou, Henan 450000, China
2Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
3Institute of Computing Technology, Chinese Academy of Sciences, Beijing
4Key Laboratory of Precision and Intelligent Chemistry,University of Science and Technology of China, Hefei,Anhui 230026, China
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Abstract
Quantum Computing is believed to be the ultimate solution for quantum chemistry problems. Before the advent of large-scale, fully fault-tolerant quantum computers, the variational quantum eigensolver (VQE) is a promising heuristic quantum algorithm to solve real world quantum chemistry problems on near-term noisy quantum computers. Here we propose a highly parallelizable classical simulator for VQE based on the matrix product state representation of quantum state, which significantly extend the simulation range of the existing simulators. Our simulator seamlessly integrates the quantum circuit evolution into the classical auto-differentiation framework, thus the gradients could be computed efficiently similar to the classical deep neural network, with a scaling that is independent of the number of variational parameters. As applications, we use our simulator to study commonly used small molecules such as HF, HCl, LiH and H$_2$O, as well as larger molecules CO$_2$, BeH$_2$ and H$_4$ with up to $40$ qubits. The favorable scaling of our simulator against the number of qubits and the number of parameters could make it an ideal testing ground for near-term quantum algorithms and a perfect benchmarking baseline for oncoming large scale VQE experiments on noisy quantum computers.
Featured image: (a) Decomposition of the wavefuction with an MPS. (b) Schematic of the memory-efficient (reversible) back-propagation algorithm for evaluating energy gradients with respect to circuit parameters. Quantum states marked in orange are to be stored in memory.
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Cited by
[1] Hyeongjin Kim, Matthew T. Fishman, and Dries Sels, “Variational adiabatic transport of tensor networks”, arXiv:2311.00748, (2023).
[2] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, “Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation”, Science China Physics, Mechanics, and Astronomy 66 5, 250302 (2023).
[3] Marcel Niedermeier, Jose L. Lado, and Christian Flindt, “Tensor-Network Simulations of Noisy Quantum Computers”, arXiv:2304.01751, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-12-05 12:11:07). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2023-12-05 12:11:05).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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- Source: https://quantum-journal.org/papers/q-2023-12-04-1192/
