Identification of Non-Markovian Environments for Spin Chains

Abstract

Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this paper, we propose a gradient algorithm for identifying the correlations in terms of timevarying damping rate functions in a time-convolution-less master equation for spin chains. By measuring time trace observables of the system, the identification procedure can be formulated as an optimization problem. The gradient algorithm is designed based on a calculation of the derivative of an objective function with respect to the damping rate functions, whose effectiveness is shown in a comparison to a differential approach for a two-qubit spin chain. I. INTRODUCTIONTo exactly process quantum information, accurate models, including parameters, structures, and descriptions of dynamics, for quantum information carriers are required. With these models, sophisticated feedback control strategies can be designed, for example, feedback stabilization of a number state in a cavity [1], preservation of quantum coherence and entanglement for qubit systems [2] and linear quantum systems [3], or coherent feedback rejection of quantum colored noise [4], [5].However, in practice, an accurate model may not be obtainable since parts of the parameters, structures or dynamics of the quantum system may not be well understood. This would lead to unexpected experimental results or degraded control performance of a quantum control system. For example, in a recent experiment on quantum dots [6], a calculation based on the theoretical model has a discrepancy from the experimental data on the broadened resonator line-width under suitable parameters, which means that some unknown dynamics of the system are not included in the model. Correspondingly, it is shown that degraded estimation performance can be observed due to ignorance of a noise model for a quantum system [7]. Hence, the problem of how to determine the unknown parameters, structures or dynamics of a "dark" quantum system is an

Identification of Time-Varying Decoherence Rates for Open Quantum Systems

“…A algorithm in Ref. [21] Current algorithm I. It is evident that the current algorithm uses fewer iterations and less time to achieve the same accuracy.…”

“…[32] for su(2), su(3) and su(4) for given basis and we also give these structure constants of su(4) in the Appendix B. Note that because the decoherence rates r jl (t) are time-varying, both A(t) and b(t) are time-varying real matrices [21].…”

“…Ref. [21] studied the same model by engaging a direct gradient algorithm in the time domain. Setting the initial conditions and the termination conditions as the same, we can obtain the number of iterations and time consumed of This work is licensed under a Creative Commons Attribution 4.0 License.…”

“…In Ref. [21], a direct gradient algorithm has been developed to identify the non-Markovian environment for spin chains by time-local master equations. Other parameter estimation algorithms for quantum dynamics were proposed in Refs.…”

“…[22]- [24]. The time-varying decoherence rates are important to understand the correlations of environments for Markovian and non-Markovian open quantum systems [21], [46]. In addition, we can measure the non-Markovianity of open quantum system from time-varying decoherence rates [29], [30], which can give insights into the nature of non-Markovian effects.…”