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Optimizing two-qubit gates for ultracold atoms using Fermi-Hubbard models

Juhi Singh1,2,*, Jan A.P. Reuter1,2, Tommaso Calarco1,2,3, Felix Motzoi1,2, and Robert Zeier1,†

  • *Contact author: j.singh@fz-juelich.de
  • †Contact author: r.zeier@fz-juelich.de
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Phys. Rev. Applied 24, 034007 – Published 3 September, 2025

DOI: https://doi.org/10.1103/xqzw-m27l

Abstract

Ultracold atoms trapped in optical lattices have emerged as a scalable and promising platform for quantum simulation and computation; however, gate speeds remain a significant limitation for practical applications. In this work, we employ quantum optimal control to design fast, collision-based two-qubit gates within a superlattice based on a Fermi-Hubbard description, reaching errors in the range 10−3 for realistic parameters. Numerically optimizing the lattice depths and the scattering length, we effectively manipulate hopping and interaction strengths intrinsic to the Fermi-Hubbard model. Our results provide five times shorter gate durations by allowing for higher energy bands in the optimization, suggesting that standard modeling with a two-band Fermi-Hubbard model is insufficient for describing the dynamics of fast gates, and we find that four to six bands are required. Additionally, we achieve nonadiabatic gates by employing time-dependent lattice depths rather than using only fixed depths. The optimized control pulses not only maintain high efficacy in the presence of laser-intensity and phase noise but also result in negligible interwell couplings.

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Phys. Rev. Applied 24, 034007– Published 3 September, 2025
  • Received 10 March 2025
  • Revised 17 June 2025
  • Accepted 25 July 2025
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