paper

Learning efficient decoders for quasi-chaotic quantum scramblers

arXiv:2212.11338 · doi:10.1103/PhysRevA.109.022429

Abstract

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 -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 -doped Clifford circuit can be decomposed into two Clifford circuits that sandwich a local unitary operator , i.e., . The local unitary operator contains non-Clifford gates and acts nontrivially on at most qubits. As simple corollaries, the gate complexity of the -doped Clifford circuit is , and it admits a efficient process tomography using resources.

arXiv commentCorrected the typos and emphasized several results on learning Clifford circuits that were previously overlooked in the previous version

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