Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems

Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, Peter Zoller.

We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present various strategies to learn the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare different ansätze based on an experimentally accessible “learning error” which we consider as a function of the number of runs of the experiment. Initially, the learning error decreasing with the inverse square root of the number of runs, as the error in the reconstructed parameters is dominated by shot noise. Eventually the learning error remains constant, allowing us to recognize missing ansatz terms. A central aspect of our approach is to (re-)parametrize ansätze by introducing and varying the dependencies between parameters. This allows us to identify the relevant parameters of the system, thereby reducing the complexity of the learning task. Importantly, this (re-)parametrization relies solely on classical post-processing, which is compelling given the finite amount of data available from experiments. A distinguishing feature of our approach is the possibility to learn the Hamiltonian, without the necessity of learning the complete Liouvillian, thus further reducing the complexity of the learning task. We illustrate our method with two, experimentally relevant, spin models.

Cite as BibTex

title={Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems},
author={Tobias Olsacher and Tristan Kraft and Christian Kokail and Barbara Kraus and Peter Zoller},

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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.