Approximation of Reachable Set for Coherently Controlled Open Quantum Systems: Application to Quantum State Engineering

Abstract

Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets for coherently controlled dissipative systems, which is very useful for assessing control performances. We apply this to a two-qubit nuclear magnetic resonance spin system and implement some tasks of quantum control in open systems at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudo-pure states. Our work shows interesting and promising applications of environment-assisted quantum dynamics.

Extensively revised and improved version. 13 pages. All comments are welcome. Includes Supplemental Material

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• Controlling NMR spin systems for quantum computation
• Algorithmic Cooling of Nuclear Spin Pairs using a Long-Lived Singlet State
• Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls
• Dual-Capability Machine Learning Models for Quantum Hamiltonian Parameter Estimation and Dynamics Prediction
• SpinQ Gemini: a desktop quantum computer for education and research
• Initial-state-dependent quantum speed limit for dissipative state preparation: Framework and optimization
• Control limit on quantum state preparation under decoherence
• Optimal Bounds on State Transfer Under Quantum Channels with Application to Spin System Engineering