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Quasi Monte Carlo method for linear combination unitaries via classical postprocessing

Yuya Kawamata1,*, Kosuke Mitarai1,2,†, and Keisuke Fujii1,2,3,‡

  • *Contact author: u597035b@ecs.osaka-u.ac.jp
  • †Contact author: mitarai.kosuke.es@osaka-u.ac.jp
  • ‡Contact author: fujii.keisuke.es@osaka-u.ac.jp
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Phys. Rev. Research 8, 023161 – Published 13 May, 2026

DOI: https://doi.org/10.1103/nmky-mykb

Abstract

We propose the quasi Monte Carlo method for linear combination of unitaries via classical postprocessing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator F(A) as F(A)=∫Vf(t)G(A,t)dt, where each G(A,t) is proportional to a unitary operator. On a quantum device, Re[Tr(G(A,t)ρ)] can be estimated using the Hadamard test and then combined through classical integration, allowing for the realization of nonunitary functions with reduced circuit depth. While previous studies have employed the Monte Carlo method or the trapezoid rule to evaluate the integral in LCU-CPP, we show that the quasi Monte Carlo method can achieve even lower errors. In two numerical experiments, ground-state property estimation and Green’s function estimation, the quasi Monte Carlo method achieves the lowest errors with a number of Hadamard test shots per unitary that is practical for real hardware implementations. These results indicate that quasi Monte Carlo is an effective integration strategy within the LCU-CPP framework.

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Phys. Rev. Research 8, 023161– Published 13 May, 2026
  • Received 19 September 2025
  • Accepted 18 April 2026
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