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  • Letter
  • Open Access

Bias-field digitized counterdiabatic quantum optimization

Alejandro Gomez Cadavid1,2, Archismita Dalal1, Anton Simen1,2, Enrique Solano1,*, and Narendra N. Hegade1,†

  • 1Kipu Quantum GmbH, Greifswalderstrasse 212, 10405 Berlin, Germany
  • 2Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain

  • *Contact author: enr.solano@gmail.com
  • †Contact author: narendrahegade5@gmail.com
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Phys. Rev. Research 7, L022010 – Published 9 April, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022010

Abstract

We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground-state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground-state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3× better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin glass on a heavy-hexagonal lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.

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Phys. Rev. Research 7, L022010– Published 9 April, 2025
  • Received 15 July 2024
  • Accepted 27 February 2025
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