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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.03234 |
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| _version_ | 1866908848247275520 |
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| author | Kim, Ha Eum Kim, Andrew D. Lee, Jong Yeon |
| author_facet | Kim, Ha Eum Kim, Andrew D. Lee, Jong Yeon |
| contents | Quantum chaos is commonly assessed through probe-dependent signatures that need not coincide. Recently, a dissipative signature was proposed for chaotic Floquet systems, where infinitesimal bulk dissipation induces a non-zero constant intrinsic relaxation rate quantified by the Liouvillian gap. This raises a question: what minimal departure from Clifford dynamics is required to generate such intrinsic relaxation? To address this, we study a Floquet two-qubit Clifford circuit doped with Haar-random single-qubit gates and subject to local dissipation of strength $γ$. We find a structure-dependent crossover. The undoped iSWAP-class circuit exhibits a weak-dissipation singularity, with a gap that grows with $N$ for any $γ>0$. Haar doping preserves this undoped-like growth for any subextensive doping pattern. At finite doping density, there exist patterns that yield an $\mathcal{O}(1)$ gap for any fixed $γ$ as $N\to\infty$, yet remain singular as $γ\to0^+$. Because our bounds depend only on the spatial doping pattern, they remain valid even when the Haar rotations are independently redrawn each Floquet period. Overall, our findings provide a circuit-level perspective on intrinsic relaxation, and thus irreversibility, in open many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits Kim, Ha Eum Kim, Andrew D. Lee, Jong Yeon Quantum Physics Statistical Mechanics Quantum chaos is commonly assessed through probe-dependent signatures that need not coincide. Recently, a dissipative signature was proposed for chaotic Floquet systems, where infinitesimal bulk dissipation induces a non-zero constant intrinsic relaxation rate quantified by the Liouvillian gap. This raises a question: what minimal departure from Clifford dynamics is required to generate such intrinsic relaxation? To address this, we study a Floquet two-qubit Clifford circuit doped with Haar-random single-qubit gates and subject to local dissipation of strength $γ$. We find a structure-dependent crossover. The undoped iSWAP-class circuit exhibits a weak-dissipation singularity, with a gap that grows with $N$ for any $γ>0$. Haar doping preserves this undoped-like growth for any subextensive doping pattern. At finite doping density, there exist patterns that yield an $\mathcal{O}(1)$ gap for any fixed $γ$ as $N\to\infty$, yet remain singular as $γ\to0^+$. Because our bounds depend only on the spatial doping pattern, they remain valid even when the Haar rotations are independently redrawn each Floquet period. Overall, our findings provide a circuit-level perspective on intrinsic relaxation, and thus irreversibility, in open many-body systems. |
| title | Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2602.03234 |