Geometric correspondence of noisy quantum dynamics and universal robust quantum gates

Yong-Ju Hai; Yao Song; Junning Li; Junkai Zeng; Xiu-Hao Deng

doi:10.1103/PhysRevApplied.23.054002

Geometric correspondence of noisy quantum dynamics and universal robust quantum gates

Yong-Ju Hai
, Yao Song
, Junning Li
, Junkai Zeng
, Xiu-Hao Deng^*

^*Corresponding author for this work

Department of Physics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

40 Downloads (CityUHK Scholars)

Abstract

Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we introduce the concept of quantum error evolution diagrams (QEEDs). QEEDs establish a dual correspondence between driven noisy quantum dynamics and geometric space curves, providing quantitative geometric metrics to assess the severity of the noises. This framework enables the design of universal robust quantum gates that correct errors induced by generic noise. Additionally, we present a protocol for constructing a universal set of single- and two-qubit robust quantum gates with simple and smooth control pulses of arbitrary length and fidelities exceeding 99.99% across a wide range of noise strengths. Our work provides new insights into the geometric nature of noisy quantum dynamics and paves the way for developing strategies to dynamically correct quantum errors. © 2025 American Physical Society.

Original language	English
Article number	054002
Journal	Physical Review Applied
Volume	23
Issue number	5
Online published	1 May 2025
DOIs	https://doi.org/10.1103/PhysRevApplied.23.054002
Publication status	Published - May 2025

Funding

X.H.D. conceived and oversaw the project. Y.J.H. and X.H.D. derived the theory, designed the protocols, and wrote the paper. Y.J.H. did all the coding and numerical simulations. Y.S., J.L., and J.Z. gave some suggestions on the algorithm. All authors contributed to the discussions. We thank Yu He, Fei Yan for suggestions on the simulations of the realistic models and Qihao Guo, Yuanzhen Chen for fruitful discussions. This work was supported by the Key-Area Research and Development Program of Guang-Dong Province (Grant No. 2018B030326001), the National Natural Science Foundation of China (U1801661), the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the Natural Science Foundation of Guangdong Province (2017B030308003), and Shenzhen Science and Technology Program (KQTD20200820113010023).

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Hai, Y.-J., Song, Y., Li, J., Zeng, J., & Deng, X.-H. (2025). Geometric correspondence of noisy quantum dynamics and universal robust quantum gates. Physical Review Applied, 23(5), Article 054002. https://doi.org/10.1103/PhysRevApplied.23.054002 The copyright of this article is owned by American Physical Society.

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title = "Geometric correspondence of noisy quantum dynamics and universal robust quantum gates",

abstract = "Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we introduce the concept of quantum error evolution diagrams (QEEDs). QEEDs establish a dual correspondence between driven noisy quantum dynamics and geometric space curves, providing quantitative geometric metrics to assess the severity of the noises. This framework enables the design of universal robust quantum gates that correct errors induced by generic noise. Additionally, we present a protocol for constructing a universal set of single- and two-qubit robust quantum gates with simple and smooth control pulses of arbitrary length and fidelities exceeding 99.99\% across a wide range of noise strengths. Our work provides new insights into the geometric nature of noisy quantum dynamics and paves the way for developing strategies to dynamically correct quantum errors. {\textcopyright} 2025 American Physical Society.",

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AU - Hai, Yong-Ju

AU - Song, Yao

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PY - 2025/5

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N2 - Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we introduce the concept of quantum error evolution diagrams (QEEDs). QEEDs establish a dual correspondence between driven noisy quantum dynamics and geometric space curves, providing quantitative geometric metrics to assess the severity of the noises. This framework enables the design of universal robust quantum gates that correct errors induced by generic noise. Additionally, we present a protocol for constructing a universal set of single- and two-qubit robust quantum gates with simple and smooth control pulses of arbitrary length and fidelities exceeding 99.99% across a wide range of noise strengths. Our work provides new insights into the geometric nature of noisy quantum dynamics and paves the way for developing strategies to dynamically correct quantum errors. © 2025 American Physical Society.

AB - Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we introduce the concept of quantum error evolution diagrams (QEEDs). QEEDs establish a dual correspondence between driven noisy quantum dynamics and geometric space curves, providing quantitative geometric metrics to assess the severity of the noises. This framework enables the design of universal robust quantum gates that correct errors induced by generic noise. Additionally, we present a protocol for constructing a universal set of single- and two-qubit robust quantum gates with simple and smooth control pulses of arbitrary length and fidelities exceeding 99.99% across a wide range of noise strengths. Our work provides new insights into the geometric nature of noisy quantum dynamics and paves the way for developing strategies to dynamically correct quantum errors. © 2025 American Physical Society.

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Geometric correspondence of noisy quantum dynamics and universal robust quantum gates

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