Bilinear dynamic mode decomposition for quantum control
arXiv:2010.14577 · doi:10.1088/1367-2630/abe972
Abstract
Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates non-linear dynamics with linear operators. In comparison with many machine learning paradigms, it requires minimal data and the biDMD model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.
16 pages, 7 figures
References in corpus (35)
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- On Dynamic Mode Decomposition: Theory and Applications
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- NMR Techniques for Quantum Control and Computation
- The Magnus expansion and some of its applications
- Control of quantum phenomena: Past, present, and future
- Prescription for experimental determination of the dynamics of a quantum black box
- Training Schrödinger's cat: quantum optimal control
- Quantum control theory and applications: A survey
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Optimal control technique for Many Body Quantum Systems dynamics
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Quantum certification and benchmarking
- Practical characterization of quantum devices without tomography
- Reinforcement Learning in Different Phases of Quantum Control
- Self-Consistent Quantum Process Tomography
- Modeling and Control of Quantum Systems: An Introduction
- Experimental Quantum Hamiltonian Learning
- Efficient measurement of quantum dynamics via compressive sensing
- Hamiltonian Learning and Certification Using Quantum Resources
- Efficient learning of quantum noise
- Experimental neural network enhanced quantum tomography
- Quantum Hamiltonian identification from measurement time traces
- Adaptive hybrid optimal quantum control for imprecisely characterized systems
- High-Fidelity Single-Shot Toffoli Gate via Quantum Control
- Data-Driven Model Predictive Control using Interpolated Koopman Generators
- Learning in Quantum Control: High-Dimensional Global Optimization for Noisy Quantum Dynamics
- Efficient estimation of nearly sparse many-body quantum Hamiltonians
- Efficient and feasible state tomography of quantum many-body systems
- Tensor-based dynamic mode decomposition
- Local-measurement-based quantum state tomography via neural networks
- High-fidelity software-defined quantum logic on a superconducting qudit
- Complete Quantum-State Tomography with a Local Random Field
- Tensor network approaches for learning non-linear dynamical laws
- Quantum System Compression: A Hamiltonian Guided Walk Through Hilbert Space
Cited by in corpus (12)
- Model predictive control for robust quantum state preparation
- Koopman analysis of quantum systems
- Forecasting long-time dynamics in quantum many-body systems by dynamic mode decomposition
- HAVOK Model Predictive Control for Time-Delay Systems with Applications to District Heating
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
- Dynamical systems and complex networks: A Koopman operator perspective
- High-Fidelity Digital Twin Data Models by Randomized Dynamic Mode Decomposition and Deep Learning with Applications in Fluid Dynamics
- Schrodinger dynamics and Berry phase of undulatory locomotion
- A unifying framework for tangential interpolation of structured bilinear control systems
- Exact Model Reduction for Continuous-Time Open Quantum Dynamics
- Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods
- Multiclass classification of dephasing channels