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Approximate quadratization of high-order Hamiltonians for combinatorial quantum optimization

Sabina Drăgoi1,2,*, Alberto Baiardi2, and Daniel J. Egger2

  • 1Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
  • 2IBM Quantum, IBM Research–Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland

  • *Contact author: sdragoi@ethz.ch
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Phys. Rev. Research 8, 023159 – Published 12 May, 2026

DOI: https://doi.org/10.1103/9rc4-vj11

Abstract

Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from appropriately prepared Ansatz quantum circuits. However, current quantum computers are limited by their qubit count, connectivity, and noise. This is particularly restrictive when considering optimization problems beyond the quadratic order. Here, we introduce Ansätze based on an approximate quadratization of high-order Hamiltonians that do not incur a qubit overhead. The price paid is a loss in the quality of the noiseless solution. Crucially, these approximations yield shallower Ansätze that are more robust to noise than the standard Quantum Approximate Optimization Algorithm one. We show this through simulations with variable noise strengths. Furthermore, we also propose a noise-aware Ansatz design method for quadratic optimization problems. This method implements only a portion of the target Hamiltonian by limiting the number of layers of swap gates in the Ansatz. We find that for both problem types, under noise, our approximate implementation of the full problem structure can significantly enhance the solution quality. Our work opens a path to enhance the solution quality that approximate quantum optimization achieves on noisy hardware.

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Phys. Rev. Research 8, 023159– Published 12 May, 2026
  • Received 21 November 2025
  • Accepted 6 April 2026
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