Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)

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Magic-Resource Generating Power of Quantum Channels

Authors
Xiaohui Li1, *
1Institute of Mathmatics Hnas, Henan Academy of Sciences, Zhengzhou, 450046, China
*Corresponding author. Email: lixiaohui@hnas.ac.cn
Corresponding Author
Xiaohui Li
Available Online 2 August 2024.
DOI
10.2991/978-94-6463-463-1_8How to use a DOI?
Keywords
magic-resource; stabilizer formalism; qutrit T-gate
Abstract

In the stabilizer formalism of quantum error correction and fault-tolerant quantum computation, stabilizer states, as common eigenstates (with the eigenvalue 1) of operators in maximal Abelian subgroups of the Pauli group, play the role of classical states, while magic (non-stabilizer) states are quantum resources enabling universal quantum computation when injected into stabilizer circuits. The natural issue arises as how to characterize and quantify the ability of quantum channels (including quantum gates) in generating magic resource (non-stabilzerness) from stabilizer states. In this work, we introduce two intuitive quantities characterizing magic-resource generating power of quantum channels and reveal their basic properties. We evaluate these quantifies for several prototypical quantum channels and quantum gates. In particular, we demonstrate that the qubit T-gate (i.e., π/8-gate) and its qutrit generalization are optimal in generating magic resource in a class of diagonal unitaries. This highlights the significance of the T-gate and its extensions from a resource-theoretic perspective and provides a theoretical support of their wide applications in stabilizer quantum computation.

Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
Series
Advances in Physics Research
Publication Date
2 August 2024
ISBN
978-94-6463-463-1
ISSN
2352-541X
DOI
10.2991/978-94-6463-463-1_8How to use a DOI?
Copyright
© 2024 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Xiaohui Li
PY  - 2024
DA  - 2024/08/02
TI  - Magic-Resource Generating Power of Quantum Channels
BT  - Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
PB  - Atlantis Press
SP  - 104
EP  - 121
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-463-1_8
DO  - 10.2991/978-94-6463-463-1_8
ID  - Li2024
ER  -