Impact of Clifford operations on non-stabilizing power and quantum chaos
Year: 2026
Authors: Varikuti N.D., Bandyopadhyay S., Hauke P.
Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR, INO, Via Sommarive 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommarive 14, I-38123 Trento, Italy; INFN TIFPA, Trento Inst Fundamental Phys & Applicat, Via Sommar 14, I-38123 Trento, Italy; Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy.
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 nonstabilizing 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 nonstabilizing 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.
Journal/Review: QUANTUM
Volume: 10 Pages from: 2017-1 to: 2017-31
More Information: N.D.V. acknowledges useful discussions with Arul Lakshminarayan and Shraddhanjali Choudhury on entangling power and quantum chaos. This project has received funding from the Italian Ministry of University and Research (MUR) through project DYNAMITE QUANTERA2_00056, in the frame of ERANET COFUND QuantERA II – 2021 call co-funded by the European Union (H2020, GA No 101017733) ; the European Union-Next Generation EU, Mission 4, Component 2-CUP E53D23002240006, and CARITRO through project SQuaSH. This project was supported by the European Union under Horizon Europe Programme-Grant Agreement 101080086-NeQST; the Swiss State Secretariat for Education, Research and lnnovation (SERI) under contract number UeMO19-5.1; the Provincia Autonoma di Trento, and Q@TN, the joint lab between University of Trento, FBK Fondazione Bruno Kessler, INFN National Institute for Nuclear Physics, and CNR National Research Council. S.B. acknowledges CINECA for use of HPC resources under Italian SuperComputing Resource Allocation- ISCRA Class C Projects No. DISYK-HP10CGNZG9 and DeepSYK-HP10CAD1L3. Views and opinions expressed are however those of the author (s) only and do not necessarily reflect those of the European Union or of the Ministry of University and Research. Neither the European Union nor the granting authority can be held responsible for them.KeyWords: Renormalization-group; State; ErrorDOI: 10.22331/q-2026-03-10-2017Citations: 2data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2026-04-19References taken from IsiWeb of Knowledge: (subscribers only)
