Quantum counterdiabatic driving with local control (2403.01854v1)
Abstract: Suppression of diabatic transitions in quantum adiabatic evolution stands as a significant challenge for ground state preparations. Counterdiabatic driving has been proposed to compensate for diabatic losses and achieve shortcut to adiabaticity. However, its implementation necessitates the generation of adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local drivings in many-body systems. In this work, we consider local counterdiabatic (LCD) driving with approximate adiabatic gauge potential. Using transverse-field Ising model as an example, we present an in-depth study of the performance and optimization of LCD protocols. We then propose a novel two-step protocol based on LCD and simple local single-body control to further improve the performance. The optimization of these LCD-based protocols does not require knowledge of instantaneous Hamiltonians, and only additional local driving is involved. To benchmark the performance of LCD and the proposed local control-enhanced LCD technique, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.
- T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).
- D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, Proceedings of the National Academy of Sciences 114, 10.1073/pnas.1619826114 (2017).
- M. V. Berry, Transitionless quantum driving, Journal of Physics A: Mathematical and Theoretical 42, 365303 (2009).
- Supplementary material of the manuscript.
- S. Morawetz and A. Polkovnikov, Efficient paths for local counterdiabatic driving (2024), arXiv:2401.12287 [quant-ph] .
- A. Hartmann and W. Lechner, Rapid counter-diabatic sweeps in lattice gauge adiabatic quantum computing, New Journal of Physics 21, 043025 (2019).
- A. del Campo, Shortcuts to adiabaticity by counterdiabatic driving, Phys. Rev. Lett. 111, 100502 (2013).
- A. del Campo, M. M. Rams, and W. H. Zurek, Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum ising model, Phys. Rev. Lett. 109, 115703 (2012).
- A. del Campo and K. Sengupta, Controlling quantum critical dynamics of isolated systems, The European Physical Journal Special Topics 224, 189 (2015).
- S. A. Moses et al., A race track trapped-ion quantum processor, arXiv:2305.03828 (2023).
- N. N. Hegade, X. Chen, and E. Solano, Digitized counterdiabatic quantum optimization, Physical Review Research 4, 10.1103/physrevresearch.4.l042030 (2022).
- T. Hogg and D. Portnov, Quantum optimization, Information Sciences 128, 181 (2000).
- E. Farhi, J. Goldstone, and S. Gutmann, A Quantum Approximate Optimization Algorithm, arXiv (2014), arXiv:1411.4028 [quant-ph] .
- J. Wurtz and P. J. Love, Counterdiabaticity and the quantum approximate optimization algorithm, Quantum 6, 635 (2022).
- K. Takahashi and A. del Campo, Shortcuts to adiabaticity in krylov space, Physical Review X 14, 10.1103/physrevx.14.011032 (2024).
- B. Bhattacharjee, A lanczos approach to the adiabatic gauge potential (2023), arXiv:2302.07228 [quant-ph] .
- D. Sels and A. Polkovnikov, Thermalization of dilute impurities in one-dimensional spin chains, Phys. Rev. X 13, 011041 (2023).
- R. P. Brent, An algorithm with guaranteed convergence for finding a zero of a function, The computer journal 14, 422 (1971).
- M. J. D. Powell, A direct search optimization method that models the objective and constraint functions by linear interpolation, in Advances in Optimization and Numerical Analysis, edited by S. Gomez and J.-P. Hennart (Springer Netherlands, Dordrecht, 1994) pp. 51–67.