Learning efficient decoders for quasichaotic quantum scramblers

作者：Lorenzo Leone, Salvatore F. E. Oliviero, Seth Lloyd, Alioscia Hamma · 发表于：Physical Review A · 年份：2024 · DOI：10.1103/physreva.109.022429 · 被引用次数：40 · 研究领域：Quantum Computing Algorithms and Architecture、Quantum Information and Cryptography、Quantum many-body systems

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics. Unscrambling this information is possible given perfect knowledge of the scrambler [arXiv:1710.03363]. We show that one can retrieve the scrambled information even without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Remarkably, the decoder is classical in the sense that it can be efficiently represented on a classical computer as a Clifford operator. It is striking that a classical decoder can retrieve with fidelity one all the information scrambled by a random unitary that cannot be efficiently simulated on a classical computer, as long as there is no full-fledged quantum chaos. This result shows that one can learn the salient properties of quantum unitaries in a classical form and sheds a new light on the meaning of quantum chaos. Furthermore, we obtain results concerning the algebraic structure of $t$-doped Clifford circuits, i.e., Clifford circuits containing $t$ non-Clifford gates, their gate complexity, and learnability that are of independent interest. In particular, we show that a $t$-doped Clifford circuit ${U}_{t}$ can be decomposed into two Clifford circuits ${U}_{0},{U}_{0}^{\ensuremath{'}}$ that sandwich a local unitary operator ${u}_{t}$, i.e., ${U}_{t}={U}_{0}{u}_{t}{U}_{0}^{\ensuremath{'}}$. The local unitary operator ${u}_{t}...