Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians

Keith R. Fratus; Kirsten Bark; Nicolas Vogt; Juha Leppäkangas; Sebastian Zanker; Michael Marthaler; Jan-Michael Reiner

doi:10.22331/q-2025-09-11-1854

Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians

Keith R. Fratus, Kirsten Bark, Nicolas Vogt, Juha Leppäkangas, Sebastian Zanker, Michael Marthaler, and Jan-Michael Reiner

HQS Quantum Simulations GmbH, Rintheimer Straße 23, 76131 Karlsruhe, Germany

Published:	2025-09-11, volume 9, page 1854
Editor:	Jordi Tura
Eprint:	arXiv:2210.11371v3
Doi:	https://doi.org/10.22331/q-2025-09-11-1854
Citation:	Quantum 9, 1854 (2025).

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Abstract

We consider the extent to which a Trotterized time evolution implemented on a quantum computer is altered by the presence of decoherence. Given a specific set of assumptions regarding the manner in which noise processes acting on such a device can be modeled at the circuit level, we show how the effects of noise can be reinterpreted as a shift to the dynamics of the original system being simulated. In particular, we find that this shift can be described through the use of static Lindblad noise terms, which act in addition to the original unitary dynamics. The form of these noise terms depends not only on the underlying noise processes occurring on the device, but also on the original unitary dynamics, as well as the manner in which these dynamics are simulated on the device, i.e., the choice of quantum algorithm. We call this effectively simulated open quantum system the noisy algorithm model. Our results are confirmed through numerical analysis.

Featured image: An initially noise-free, Hamiltonian system is simulated on a noisy quantum computer, which, under a specific set of assumptions regarding the manner in which noise processes acting on such a device can be modeled at the circuit level, gives rise to the "noisy algorithm model." This noisy algorithm model is described by an effective Liouvillian time-evolution super-operator with both Hamiltonian and Linbladian parts.

Popular summary

Quantum computers promise to open up new possibilities for the simulation of physical systems, which will have applications in the fields of chemistry, pharmaceuticals, materials science, and beyond. However, current quantum computers still suffer from engineering limitations which allow for interference from the environment, typically referred to as "noise." This noise can affect the accuracy that can be reached when performing such simulations, calling into question whether current quantum computers have any practical utility.

However, for much the same reasons that quantum computers are effected by noise, the physical systems which we hope to simulate with them are often also affected by similar types of noise, and a fully realistic simulation of their behaviour should incorporate this fact. This then leads to the natural question: can the noise on quantum computers actually be utilized as a resource for simulating the noisy portion of the dynamics of these systems? That is to say, if we perform a naive simulation of the noise-free physical system, but we do so on a noisy quantum computer, can we interpret the results of this simulation not as a defective result for the noise-free system, but rather as the successful simulation of the more realistic, noisy version of the physical system?

We address this question for a particular type of physical system (a “quantum spin system”), and we find that such a reinterpretation is indeed possible. The majority of our results in this work focus on developing the precise mapping between the type of noise on the quantum computer, and the resulting type of noise on the effectively simulated noisy system. This mapping is in fact non-trivial, and depends not only on the noise present on the quantum computer, but also the specific system being simulated, as well as the precise manner in which we simulate it on the quantum computer. Our results represent an important step towards the simulation of real physical systems on quantum computers.

► BibTeX data

@article{Fratus2025describing,
  doi = {10.22331/q-2025-09-11-1854},
  url = {https://doi.org/10.22331/q-2025-09-11-1854},
  title = {Describing {T}rotterized {T}ime {E}volutions on {N}oisy {Q}uantum {C}omputers via {S}tatic {E}ffective {L}indbladians},
  author = {Fratus, Keith R. and Bark, Kirsten and Vogt, Nicolas and Lepp{\"{a}}kangas, Juha and Zanker, Sebastian and Marthaler, Michael and Reiner, Jan-Michael},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1854},
  month = sep,
  year = {2025}
}

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