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Accurate models of the dynamics of quantum circuits are essential foroptimizing and advancing quantum devices. Since first-principles models ofenvironmental noise and dissipation in real quantum systems are oftenunavailable, deriving accurate models from measured time-series data iscritical. However, identifying open quantum systems poses significantchallenges: powerful methods from systems engineering can perform poorly beyondweak damping (as we show) because they fail to incorporate essentialconstraints required for quantum evolution (e.g., positivity). Common methodsthat can include these constraints are typically multi-step, fitting linearmodels to physically grounded master equations, often resulting in non-convexfunctions in which local optimization algorithms get stuck in local extrema (aswe show). In this work, we solve these problems by formulating quantum systemidentification directly from data as a polynomial optimization problem,enabling the use of recently developed global optimization methods. Thesemethods are essentially guaranteed to reach global optima, allowing us for thefirst time to efficiently obtain the most accurate Markovian model for a givensystem. In addition to its practical importance, this allows us to take theerror of these Markovian models as an alternative (operational) measure of thenon-Markovianity of a system. We test our method with the spin-boson model -- atwo-level system coupled to a bath of harmonic oscillators -- for which weobtain the exact evolution using matrix-product-state techniques. We show thatpolynomial optimization using moment/sum-of-squares approaches significantlyoutperforms traditional optimization algorithms, and we show that even forstrong damping Lindblad-form master equations can provide accurate models ofthe spin-boson system.

Quantum open system identification via global optimization: Optimally accurate Markovian models of open systems from time-series data