Impact of Clifford operations on non-stabilizing power and quantum chaos
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908876780077056 |
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| author | Varikuti, Naga Dileep Bandyopadhyay, Soumik Hauke, Philipp |
| author_facet | Varikuti, Naga Dileep Bandyopadhyay, Soumik Hauke, Philipp |
| contents | Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of non-stabilizerness in circuits that mix Clifford and non-Clifford operations remains elusive. While Clifford operations do not generate non-stabilizerness, their interplay with non-Clifford gates can strongly impact the overall non-stabilizing dynamics of generic quantum circuits. In this work, we establish a direct relationship between the final non-stabilizing power and the individual powers of the non-Clifford gates, in circuits where these gates are interspersed with random Clifford operations. By leveraging this result, we unveil the thermalization of non-stabilizing power to its Haar-averaged value in generic circuits. As a precursor, we analyze two-qubit gates and illustrate this thermalization in analytically tractable systems. Extending this, we explore the operator-space non-stabilizing power and demonstrate its behavior in physical models. Finally, we examine the role of non-stabilizing power in the emergence of quantum chaos in brick-wall quantum circuits. Our work elucidates how non-stabilizing dynamics evolve and thermalize in quantum circuits and thus contributes to a better understanding of quantum computational resources and of their role in quantum chaos. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_14793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Impact of Clifford operations on non-stabilizing power and quantum chaos Varikuti, Naga Dileep Bandyopadhyay, Soumik Hauke, Philipp Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of non-stabilizerness in circuits that mix Clifford and non-Clifford operations remains elusive. While Clifford operations do not generate non-stabilizerness, their interplay with non-Clifford gates can strongly impact the overall non-stabilizing dynamics of generic quantum circuits. In this work, we establish a direct relationship between the final non-stabilizing power and the individual powers of the non-Clifford gates, in circuits where these gates are interspersed with random Clifford operations. By leveraging this result, we unveil the thermalization of non-stabilizing power to its Haar-averaged value in generic circuits. As a precursor, we analyze two-qubit gates and illustrate this thermalization in analytically tractable systems. Extending this, we explore the operator-space non-stabilizing power and demonstrate its behavior in physical models. Finally, we examine the role of non-stabilizing power in the emergence of quantum chaos in brick-wall quantum circuits. Our work elucidates how non-stabilizing dynamics evolve and thermalize in quantum circuits and thus contributes to a better understanding of quantum computational resources and of their role in quantum chaos. |
| title | Impact of Clifford operations on non-stabilizing power and quantum chaos |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2505.14793 |