Lindblad-like quantum tomography for non-Markovian quantum dynamical maps

npj Quantum Information, vol. 11

Abstract

Abstract We introduce Lindblad-like quantum tomography (LℓQT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss LℓQT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of LℓQT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.

Authors 3

1. Santiago Varona corresponding Aachen Institute for Quantum Information

   RWTH Aachen University · Consejo Superior de Investigaciones Científicas · Instituto de Física Teórica · Universidad Autónoma de Madrid

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

   Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain

2. Markus Michael Müller Aachen Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, Jülich, Germany

3. A. Bermúdez

   Consejo Superior de Investigaciones Científicas · Instituto de Física Teórica · Universidad Autónoma de Madrid

   Affiliation as printed

   Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain