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  • Open Access

Phase Estimation with Partially Randomized Time Evolution

Jakob Günther1,3, Freek Witteveen1,2,*, Alexander Schmidhuber3, Marek Miller1, Matthias Christandl1, and Aram W. Harrow3

  • 1Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
  • 2QuSoft and CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands
  • 3Center for Theoretical Physics - a Leinweber Institute, MIT, Cambridge, Massachusetts 02139, USA

  • *Contact author: f.witteveen@cwi.nl
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PRX Quantum 7, 020332 – Published 19 May, 2026

DOI: https://doi.org/10.1103/ynxb-p2xq

Abstract

Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground-state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation subroutine. In this paper we use randomization to speed up product formulas, one of the standard approaches to Hamiltonian simulation. We propose partially randomized Hamiltonian simulation methods in which some terms are kept deterministically and others are randomly sampled. We perform a detailed resource estimate for single-ancilla phase estimation using partially randomized product formulas for benchmark systems in quantum chemistry and obtain orders-of-magnitude improvements compared to other simulations based on product formulas. When applied to the hydrogen chain, we have numerical evidence that our methods exhibit asymptotic scaling with the system size that is competitive with the best known qubitization approaches.

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Popular Summary

Molecular behavior is governed by quantum mechanics, but predicting molecular properties accurately requires solving hard equations. Quantum computers could eventually do this more efficiently than classical computers, but practical advantage will require better algorithms with careful resource estimates. Our work exploits a common feature of molecular interactions: a few are strong, while many others are weak. We treat these differently. Strong interactions are kept always on, while at each algorithmic step we randomly activate only a small subset of weak interactions and leave the rest off. Repeating this sampling over many steps yields a useful output signal. Resource estimates for several molecules show that our method compares favorably with existing approaches, especially by reducing quantum circuit depth while keeping the number of qubits modest.

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Outline

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PRX Quantum 7, 020332– Published 19 May, 2026
  • Received 12 May 2025
  • Revised 16 September 2025
  • Accepted 31 March 2026
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