Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries (2401.02355v1)
Abstract: The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.
- C. Zalka, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 313 (1998).
- G. H. Low, Y. Su, Y. Tong, and M. C. Tran, “On the complexity of implementing Trotter steps,” (2022), arXiv:2211.09133 [cond-mat, physics:physics, physics:quant-ph] .
- G. H. Low and I. L. Chuang, Quantum 3, 163 (2019), arXiv:1610.06546 [quant-ph] .
- G. H. Low and I. L. Chuang, Physical Review Letters 118, 010501 (2017), arXiv:1606.02685 [quant-ph] .
- A. M. Childs and N. Wiebe, Quantum Information and Computation 12, 10.26421/QIC12.11-12, arXiv:1202.5822 [quant-ph] .
- E. Campbell, Physical Review Letters 123, 070503 (2019), arXiv:1811.08017 [quant-ph] .
- J. Preskill, Quantum 2, 79 (2018), arxiv:1801.00862 .
- Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017).
- J. C. Bridgeman and C. T. Chubb, Journal of Physics A: Mathematical and Theoretical 50, 223001 (2017).
- J. Huang, W. He, Y. Zhang, Y. Wu, B. Wu, and X. Yuan, “Tensor Network Assisted Variational Quantum Algorithm,” (2022), arXiv:2212.10421.
- A. Khan, B. K. Clark, and N. M. Tubman, “Pre-optimizing variational quantum eigensolvers with tensor networks,” (2023), 2310.12965 [cond-mat, physics:quant-ph] .
- S. Shin, Y. S. Teo, and H. Jeong, “Analyzing quantum machine learning using tensor network,” (2023), 2307.06937 [quant-ph] .
- Y. Fan, J. Liu, Z. Li, and J. Yang, “Quantum circuit matrix product state ansatz for large-scale simulations of molecules,” (2023), 2301.06376 [physics, physics:quant-ph] .
- “IBM Quantum Awards: Open Science Prize 2022,” Qiskit Community (2023), https://github.com/qiskit-community/open-science-prize-2022/tree/main.
- J. Kattemölle and J. van Wezel, Phys. Rev. B 106, 214429 (2022).
- J. S, K. A, D. M. M, S. Vishwakarma, S. Ganguly, and Y. P, “Efficient vqe approach for accurate simulations on the kagome lattice,” (2023), arXiv:2306.00467 [quant-ph] .
- L. Balents, Nature 464, 199 (2010).
- U. Schollwöck, Rev. Modern Phys. 77, 259 (2005).
- U. Schollwöck, Ann. Phys. 326, 96 (2011).
- S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
- F. Verstraete and J. I. Cirac, prb 73, 094423 (2006).
- M. B. Hastings, J. Stat. Mech. , P08024 (2007).
- MindQuantum, “Mindquantum,” .
- S.-J. Ran, Phys. Rev. A 101, 032310 (2020).
- M. S. Rudolph, J. Chen, J. Miller, A. Acharya, and A. Perdomo-Ortiz, “Decomposition of matrix product states into shallow quantum circuits,” (2022), arXiv:2209.00595 [quant-ph] .