Spectral Properties and Magic Generation in \(T\)-doped Random Clifford Circuits
محفوظ في:
| الحاوية / القاعدة: | arXiv.org (Dec 20, 2024), p. n/a |
|---|---|
| المؤلف الرئيسي: | |
| مؤلفون آخرون: | , , , , , |
| منشور في: |
Cornell University Library, arXiv.org
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | Citation/Abstract Full text outside of ProQuest |
| الوسوم: |
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| مستخلص: | We study the emergence of complexity in deep random \(N\)-qubit \(T\)-gate doped Clifford circuits, as reflected in their spectral properties and in magic generation, characterized by the stabilizer Rényi entropy. For pure (undoped) Clifford circuits, a unique periodic orbit structure in the space of Pauli strings implies peculiar spectral correlations and level statistics with large degeneracies. \(T\)-gate doping induces an exponentially fast transition to chaotic behavior, described by random matrix theory. To characterize magic generation properties of the Clifford+\(T\) ensemble, we determine the distribution of magic, as well as the average nonstabilizing power of the quantum circuit ensemble. In the dilute limit, \(N_T \ll N\), magic generation is governed by single-qubit behavior, and magic increases linearly with the number of \(T\)-gates, \(N_T\). For \(N_T\gg N\), magic distribution converges to that of Haar-random unitaries, and averages to a finite magic density, \(\mu\), \(\lim_{N\to\infty} \langle\mu\rangle_\text{Haar} = 1\). Although our numerics has large finite-size effects, finite size scaling reveals a magic density phase transition at a critical \(T\)-gate density, \(n^{*}_T = (N_T/N)^* \approx 2.41\) in the \(N \to \infty\) limit. This is in contrast to the spectral transition, where \({\cal O} (1)\) \(T\)-gates suffice to remove spectral degeneracies and to induce a transition to chaotic behavior in the thermodynamic limit. Magic is therefore a more sensitive indicator of complexity. |
|---|---|
| تدمد: | 2331-8422 |
| المصدر: | Engineering Database |