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Hamiltonian simulation with explicit formulas for digital-analog quantum computing

Mikel Garcia de Andoin1,2,*, Thorge Müller3,†, and Gonzalo Camacho3,‡

  • *Contact author: mikel.garciadeandoin@ehu.eus
  • †Contact author: thorge.mueller@dlr.de
  • ‡Contact author: gonzalo.camacho@dlr.de
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Phys. Rev. A 113, 062607 – Published 3 June, 2026

DOI: https://doi.org/10.1103/nzxg-5lbg

Abstract

Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.

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Phys. Rev. A 113, 062607– Published 3 June, 2026
  • Received 20 November 2025
  • Accepted 8 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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