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IEEE Transactions on Quantum Engineering

Identification of Time-Varying Decoherence Rates for Open Quantum Systems

Shuixin Xiao, Shibei Xue, Daoyi Dong, Jun Zhang

Published Jan 1, 2021• 10 citations
Publisher

Abstract

Parameter identification of quantum systems is a fundamental task in developing practical quantum technology. In this article, we study the identification of time-varying decoherence rates for open quantum systems. Given the measurement data of local observables, this can be formulated as an optimization problem. We expand the unknown decoherence rates into Fourier series and take the expansion coefficients as optimization variables. We then convert it into a minimax problem and apply a sequential linear programming technique to solve it. Numerical study on a two-qubit quantum system with a time-varying decoherence rate demonstrates the effectiveness of our algorithm.

DOI
10.1109/tqe.2021.3093055

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Parameter identification of quantum systems is a fundamental task in developing practical quantum technology. In this article, we study the identification of time-varying decoherence rates for open quantum systems. Given the measurement data of local observables, this can be formulated as an optimization problem. We expand the unknown decoherence rates into Fourier series and take the expansion coefficients as optimization variables. We then convert it into a minimax problem and apply a sequential linear programming technique to solve it. Numerical study on a two-qubit quantum system with a time-varying decoherence rate demonstrates the effectiveness of our algorithm.
Identifying parameters in the system Hamiltonian is a vitally important task in the development of quantum technology. This paper investigates the problem of Hamiltonian identification for closed quantum systems and develops a new algorithm to achieve the task of identifying the Hamiltonian. Under the framework of standard quantum process tomography and without prior assumptions, we first convert the problem of Hamiltonian identification into an optimization problem and then design an iterative algorithm to numerically solve this problem. Numerical results for a two-qubit system are presented to show the effectiveness of the proposed algorithm through analyzing the mean squared error.
Accurate models of the dynamics of quantum circuits are essential for optimizing and advancing quantum devices. Since first-principles models of environmental noise and dissipation in real quantum systems are often unavailable, deriving accurate models from measured time-series data is critical. However, identifying open quantum systems poses significant challenges: powerful methods from systems engineering can perform poorly beyond weak damping (as we show) because they fail to incorporate essential constraints required for quantum evolution (e.g., positivity). Common methods that can include these constraints are typically multi-step, fitting linear models to physically grounded master equations, often resulting in non-convex functions in which local optimization algorithms get stuck in local extrema (as we show). In this work, we solve these problems by formulating quantum system identification directly from data as a polynomial optimization problem, enabling the use of recently developed global optimization methods. These methods are essentially guaranteed to reach global optima, allowing us for the first time to efficiently obtain the most accurate Markovian model for a given system. In addition to its practical importance, this allows us to take the error of these Markovian models as an alternative (operational) measure of the non-Markovianity of a system. We test our method with the spin-boson model -- a two-level system coupled to a bath of harmonic oscillators -- for which we obtain the exact evolution using matrix-product-state techniques. We show that polynomial optimization using moment/sum-of-squares approaches significantly outperforms traditional optimization algorithms, and we show that even for strong damping Lindblad-form master equations can provide accurate models of the spin-boson system.
Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.
In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master equation based on which the Hamiltonian identification problem can be formulated as minimizing the distance between the real time traces of the observables and those predicted by the master equation. The unknown parameters can then be learned with a gradient descent algorithm from the measurement data. We verify the effectiveness of our algorithm in a circuit QED system described by a Jaynes-Cummings model whose Hamiltonian identification has been rarely considered. We also show that our gradient algorithm can learn the spectrum of a non-Markovian environment based on an augmented system model.
The identification of time-varying parameters (e.g., directly inaccessible in situ signals in vacuum and low-temperature environments) is prevalent for characterizing the dynamics of quantum processes. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with specially designed probe systems can the parameters be explicitly read out, and a rigorous identifiability analysis is lacking, i.e., whether the measurement data are sufficient for unambiguous identification. In this paper we formulate this problem as the invertibility of the input-output mapping associated with the quantum system for which an algebraic identifiability criterion is derived based on the system's relative degree. The invertibility analysis also leads to an inversion-based algorithm for numerically identifying the parameters, which is computationally much more efficient than nonlinear regression methods. The effectiveness of the criterion are demonstrated by numerical examples.
We present a comprehensive analytical and numerical study of time-dependent decoherence in open quantum systems, focusing on a single-qubit model with time-varying Lindblad dissipation rates. Employing a master equation framework, we derive exact solutions for the evolution of off-diagonal density matrix elements and characterize the emergence of robust pointer states. Our findings reveal an initial rapid coherence decay followed by a gradual slowdown, mirroring experimental trends observed in superconducting qubits influenced by quasiparticle dynamics and in photonic cavities subject to fluctuating environments. By incorporating real experimental parameters and validating the model through quantum simulations using QuTiP, we provide a robust quantitative tool for analyzing decoherence in quantum technologies. This extended model addresses limitations in static-rate approximations, offering insights into non-Markovian effects without resolving the measurement problem, and suggests extensions to multi-qubit systems.