Analog variational quantum simulators with long-range interactions

Current experimental quantum devices do not meet the requirements for building fault-tolerant quantum computers, but they still can be used to address many-body problems as analogue quantum simulators. Some of these platforms, like superconducting circuits [1], trapped-ions [2], Rydberg atoms [3] or ultracold atoms [4], can be engineered to have long-range interactions between its components. However, the systems simulated are constrained by the type of interactions that can be engineered in the platform.

Variational methods have been suggested as a way to go beyond this limitation [5,6]. Among the different proposals, Variational Quantum Time Evolution algorithms (VarQTE) can perform either real or imaginary time evolution within the same framework [7]. In this work we propose to use this variational approach to fully harness the tunability of the long-range interactions in analogue quantum simulators. We demonstrate how some of the limitations of VarQTE can be solved using this tunable long-range, and benchmark this advantage against fixed range quantum simulators in both imaginary and real time evolution. Furthermore, we consider analogue quantum simulators made of qubits, bosons and fermions, using tensor network methods to highlight the role of the tunable long-range as the system size increases.

In summary, our work introduces a new set of tools that can be used to compute both ground states and dynamics of complex many-body Hamiltonians using simpler analogue quantum simulators.

[1] X. Zhang et al., Science 379, 278-283 (2023).

[2] C. Kokail et al., Nature 569, 355–360 (2019).

[3] S. Ebadi et al., Nature 595, 227–232 (2021).

[4] J. Argüello-Luengo et al., Nature 574, 215–218 (2019).

[5] A. J. Daley et al., Nature 607, 667–676 (2022).

[6] C. Tabares et al., Phys. Rev. Lett. 131, 073602 (2023).

[7] X. Yuan et al., Quantum 3, 191 (2019).