Impact of Clifford operations on non-stabilizing power and quantum chaos

• URL: http://arxiv.org/abs/2505.14793v2
• Date: Sun, 13 Jul 2025 18:07:13 GMT
• Title: Impact of Clifford operations on non-stabilizing power and quantum chaos
• Abstract summary: Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation.<n>We study the generation and thermalization of non-stabilizerness in circuits that mix Clifford and non-Clifford operations.<n>Our work contributes to a better understanding of quantum computational resources and of their role in quantum chaos.
• Score: 14.37149160708975
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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