A Butterfly Effect in Encoding-Decoding Quantum Circuits

• URL: http://arxiv.org/abs/2409.16481v1
• Date: Tue, 24 Sep 2024 22:01:14 GMT
• Title: A Butterfly Effect in Encoding-Decoding Quantum Circuits
• Authors: Emanuel Dallas, Faidon Andreadakis, Paolo Zanardi,
• Abstract summary: Scrambling is measured using the bipartite algebraic out-of-time-order correlator ($mathcalA$-OTOC) In the thermodynamic limit, this system displays a textitbutterfly effect in which infinitesimal noise induces macroscopic information scrambling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of information scrambling has profoundly deepened our understanding of many-body quantum systems. Much recent research has been devote to understanding the interplay between scrambling and decoherence in open systems. Continuing in this vein, we investigate scrambling in a noisy encoding-decoding circuit model. Specifically, we consider an $L$-qubit circuit consisting of a Haar-random unitary, followed by noise acting on a subset of qubits, and then by the inverse unitary. Scrambling is measured using the bipartite algebraic out-of-time-order correlator ($\mathcal{A}$-OTOC), which allows us to track information spread between extensively sized subsystems. We derive an analytic expression for the $\mathcal{A}$-OTOC that depends on system size and noise strength. In the thermodynamic limit, this system displays a \textit{butterfly effect} in which infinitesimal noise induces macroscopic information scrambling. We also perform numerical simulations while relaxing the condition of Haar-randomness, which preliminarily suggest that this effect may manifest in a larger set of circuits.

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