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Correcting and Extending Trotterized Quantum Many-Body Dynamics

Gian Gentinetta1,2,*, Friederike Metz1,2, and Giuseppe Carleo1,2

  • *Contact author: gian.gentinetta@epfl.ch
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PRX Quantum 6, 030361 – Published 24 September, 2025

DOI: https://doi.org/10.1103/1nqt-x5xh

Abstract

A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical application is currently limited by noise and restricted scalability. In this work, we address these problems by introducing a hybrid ansatz combining the strengths of quantum and classical computational methods. Using Trotterization, we propose to evolve an initial state on the quantum computer according to a simplified Hamiltonian, focusing on terms that are difficult to simulate classically. A classical model then corrects the simulation by including the terms omitted in the quantum circuit. While the classical ansatz is optimized during the time evolution, the quantum circuit has no variational parameters. Derivatives can thus be calculated purely classically, avoiding challenges arising in the optimization of parametrized quantum circuits. We demonstrate three applications of this hybrid method. First, our approach allows us to avoid swap gates in the quantum circuit by restricting the quantum part of the ansatz to hardware-efficient terms of the Hamiltonian. Second, we can mitigate errors arising from the Trotterization of the time-evolution unitary. Finally, we can extend the system size while keeping the number of qubits in the quantum circuit constant by including additional degrees of freedom in the classical ansatz.

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Popular Summary

Predicting how quantum systems evolve in time is key to obtaining a profound understanding of the nature of physical phenomena at the microscopic scale. As solving this problem analytically is improbable, scientists rely on computational methods to perform simulations. While these methods are becoming increasingly efficient and classical computers more powerful, the laws of quantum mechanics ultimately challenge classical algorithms in simulating arbitrary quantum systems once they reach a certain scale. In this context, quantum computers can, in theory, provide an advantage. In practice, however, near-term quantum devices are still very prone to errors, which imposes strong constraints on the algorithms they can run.

In this work, we aim to simplify the quantum algorithm simulating the time evolution of complex quantum systems such that it becomes feasible to obtain interesting results even on noisy hardware. To that end, we outsource part of the calculation to a classical model, so that only the part of the system that is difficult to simulate classically but natural for the quantum computer has to be implemented on the latter. We then generate data from the simplified quantum algorithm to train the classical model, which subsequently extends the computation to simulate the entire system.

The framework presented in our work provides a general method of combining quantum and classical resources for the simulation of quantum time evolution. The formulation allows for a wide range of classical models to be employed to correct for diverse simplifications made to the quantum algorithm.

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PRX Quantum 6, 030361– Published 24 September, 2025
  • Received 9 April 2025
  • Revised 1 July 2025
  • Accepted 21 August 2025
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