Quantum Simulation of Open Quantum Dynamics via Non-Markovian Quantum State Diffusion (2404.10655v2)
Abstract: Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources. Here we introduce a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in system with non-Markovian environment. Our approach includes formulating a non-Markovian Stochastic Schr\"odinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. Following this, we utilize variational quantum simulation to capture the non-unitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated the spin-boson model and dynamic quantum phase transitions (DQPT) within transverse field Ising model (TFIM). Significantly, our findings reveal the enhanced DQPT in TFIM due to non-Markovian behavior.
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
- U. Weiss, Quantum dissipative systems, Vol. 13 (World scientific, 2012).
- V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (John Wiley & Sons, 2008).
- J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014).
- Y. Tanimura and R. Kubo, J. Phys. Soc. Jpn. 58, 101 (1989).
- Y. Tanimura, J. Phys. Soc. Jpn. 75, 082001 (2006).
- N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4600 (1995a).
- N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4611 (1995b).
- Q. Shi and E. Geva, J. Chem. Phys. 119, 12063 (2003).
- G. Cohen and E. Rabani, Phys. Rev. B 84, 075150 (2011).
- H. Wang and M. Thoss, J. Chem. Phys. 119, 1289 (2003).
- Y.-A. Yan and J. Shao, Frontiers of Physics 11, 1 (2016).
- J. Preskill, Quantum 2, 79 (2018).
- J. D. Guimarães, M. I. Vasilevskiy, and L. S. Barbosa, Quantum 8, 1242 (2024).
- P. L. Walters and F. Wang, Phys. Rev. Research. 6, 013135 (2024).
- D. Suess, A. Eisfeld, and W. Strunz, Phys. Rev. Lett. 113, 150403 (2014).
- D. Suess, W. T. Strunz, and A. Eisfeld, J. Stat. Phys. 159, 1408 (2015).
- L. Diósi and W. T. Strunz, Phys. Lett. A 235, 569 (1997).
- L. Diósi, N. Gisin, and W. T. Strunz, Phys. Rev. A 58, 1699 (1998).
- W. T. Strunz, L. Diósi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999).
- J. Jing and T. Yu, Phys. Rev. Lett. 105, 240403 (2010).
- S. Flannigan, F. Damanet, and A. J. Daley, Phys. Rev. Lett. 128, 063601 (2022).
- N. Okuma and Y. O. Nakagawa, Phys. Rev. B 105, 054304 (2022).
- M. Heyl, Physical review letters 113, 205701 (2014).
- A. Zvyagin, Low Temperature Physics 42, 971 (2016).
- M. Heyl and J. Budich, Physical Review B 96, 180304 (2017).
- M. Heyl, Europhysics Letters 125, 26001 (2019).
- R. Puebla, Physical Review B 102, 220302 (2020).
- A. Norambuena, D. Tancara, and R. Coto, European Journal of Physics 41, 045404 (2020).
- D. Dolgitzer, D. Zeng, and Y. Chen, Optics Express 29, 23988 (2021).
- X. Gao and A. Eisfeld, J. Chem. Phys. 150 (2019).
- J. R. Johansson, P. D. Nation, and F. Nori, Computer Physics Communications 183, 1760 (2012).
- J. Johansson, P. Nation, and F. Nori, Computer Physics Communications 184, 1234 (2013).
- T. Ikeda and G. D. Scholes, J. Chem. Phys. 152 (2020).
- Y. Ke and Y. Zhao, J. Chem. Phys. 145, 024101 (2016).
- K. Song, L. Song, and Q. Shi, J. Chem. Phys. 144, 224105 (2016).
- Renormalizer, https://github.com/shuaigroup/Renormalizer.
- W. Li, J. Ren, and Z. Shuai, J. Chem. Phys. 152, 024127 (2020).
- X. Zhong and Y. Zhao, J. Chem. Phys. 138, 014111 (2013).