Impact of decoherence on the fidelity of quantum gates leaving the computational subspace

Tahereh Abad; Yoni Schattner; Anton Frisk Kockum; Göran Johansson

doi:10.22331/q-2025-04-03-1684

Impact of decoherence on the fidelity of quantum gates leaving the computational subspace

Tahereh Abad¹, Yoni Schattner², Anton Frisk Kockum¹, and Göran Johansson¹

¹Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
²AWS Center for Quantum Computing, Pasadena, CA 91125, USA

Published:	2025-04-03, volume 9, page 1684
Editor:	Alioscia Hamma
Eprint:	arXiv:2302.13885v3
Doi:	https://doi.org/10.22331/q-2025-04-03-1684
Citation:	Quantum 9, 1684 (2025).

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Abstract

The fidelity of quantum operations is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In Phys. Rev. Lett. 129, 150504 (2022), we presented an analytical result for the average gate fidelity of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators, provided that the operation remains in the computational subspace throughout the time evolution. Here we generalize this expression for the average gate fidelity to include the cases where the system state temporarily leaves the computational subspace during the gate. Such gate mechanisms are integral to several quantum-computing platforms, and our formula is applicable to all of them; as examples, we employ it for the two-qubit controlled-Z gate in both superconducting qubits and neutral atoms. We also obtain the average gate fidelity for simultaneous operations applied in multiqubit systems. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.

Popular summary

Quantum computing has the potential to revolutionize fields such as cryptography, materials science, and optimization. Major technology companies, startups, and research institutions worldwide are racing to develop practical quantum computers. However, a fundamental challenge remains: errors caused by interactions with the surrounding environment, which lead to decoherence and dissipation. Even though quantum gates, the building blocks of quantum computation, have achieved fidelities above 99% in various platforms, further improvements are crucial for both near-term quantum algorithms and future fault-tolerant quantum computing.

To quantify and mitigate these errors, it is essential to understand how noise impacts gate fidelity, the standard measure of a gate’s performance. In Phys. Rev. Lett. 129, 150504 (2022), we derived general analytical formulas describing how decoherence affects gate fidelity when the quantum state remains within the computational subspace. In this manuscript, we extend this framework to account for quantum operations where the system temporarily leaves this subspace, something that is common in many quantum-computing architectures.

Our new formula expresses the impact of decoherence in terms of dissipative rates and Lindblad jump operators, providing a versatile tool for assessing error budgets in various quantum platforms. We illustrate its usefulness by applying it to key quantum gates across different hardware implementations.

By improving our understanding of how decoherence affects quantum gates beyond the computational subspace, our findings offer valuable insights for hardware characterization, algorithm design, and the overall advancement of quantum computing.

► BibTeX data

@article{Abad2025impactofdecoherence,
  doi = {10.22331/q-2025-04-03-1684},
  url = {https://doi.org/10.22331/q-2025-04-03-1684},
  title = {Impact of decoherence on the fidelity of quantum gates leaving the computational subspace},
  author = {Abad, Tahereh and Schattner, Yoni and Kockum, Anton Frisk and Johansson, G{\"{o}}ran},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1684},
  month = apr,
  year = {2025}
}

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The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 16:01:24) and SAO/NASA ADS (last updated successfully 2026-07-15 16:01:41). The list may be incomplete as not all publishers provide suitable and complete citation data.

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