Frame-Based Filter-Function Formalism for Quantum Characterization and Control

Abstract

We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the general notion of a frame and by appropriately tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and, crucially, it permits an efficient representation of the relevant control matrix elements and dynamical integrals if an appropriate finite-size frame condition is obeyed. Our frame-based formulation overcomes important limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of nonstationary noise sources, and how to effectively achieve control-driven model reduction for noise-optimized prediction and quantum gate design.

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• Filtering crosstalk from bath non-Markovianity via spacetime classical shadows
• Quantum Control Noise Spectroscopy with Optimal Suppression of Dephasing
• Noise Detection with Spectator Qubits and Quantum Feature Engineering
• SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally Correlated Environments
• Greedy versus Map-based Optimized Adaptive Algorithms for random-telegraph-noise mitigation by spectator qubits
• Path integral framework for characterizing and controlling decoherence induced by non-stationary environments on a quantum probe
• Digital noise spectroscopy with a quantum sensor
• Quantum Gates Robust to Secular Amplitude Drifts
• The Role of Bases in Quantum Optimal Control
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Quantum decoherence dynamics in stochastically fluctuating environments
• Sensing Out-of-Equilibrium and Quantum Non-Gaussian environments via induced Time-Reversal Symmetry Breaking on the quantum-probe dynamics
• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps
• On the use of total state decompositions for the study of reduced dynamics
• Imperfection analyses for random-telegraph-noise mitigation using spectator qubits
• Expedited Noise Spectroscopy of Transmon Qubits
• Quantum state-preparation control in noisy environment via most-likely paths
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems