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Halving the arbitrary rotation cost of controlled, Trotterized time evolution

William A. Simon* and Peter J. Love

  • *Contact author: william.andrew.simon@gmail.com
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Phys. Rev. A 114, 032425 – Published 9 September, 2026

DOI: https://doi.org/10.1103/h9gv-ml7w

Abstract

Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme to control a symmetric Trotterization that does not increase the number of arbitrary rotations. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to T cost in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations often dominate resource estimates for fault-tolerant implementations of quantum simulation algorithms. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.

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Phys. Rev. A 114, 032425– Published 9 September, 2026
  • Received 24 November 2025
  • Accepted 6 August 2026
Article part of CHORUS
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