Diagnosis of information scrambling from Hamiltonian evolution under decoherence

• URL: http://arxiv.org/abs/2103.05179v2
• Date: Fri, 24 Sep 2021 16:00:20 GMT
• Title: Diagnosis of information scrambling from Hamiltonian evolution under decoherence
• Authors: Tomoya Hayata, Yoshimasa Hidaka, Yuta Kikuchi
• Abstract summary: We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. We numerically simulate the time evolution of the two theories in the Hamiltonian formalism. We find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.
• Score: 1.5791732557395552
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of-time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call it Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. We find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.

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