GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
arXiv:2307.08479 · doi:10.1088/1751-8121/ace13f
Abstract
The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to coherently controlled closed and open quantum systems. In this work, we adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. In our case, the tailored or engineered environment acts on the system as control via it time-dependent decoherence rates or, equivalently, via it spectral density of the environment . To develop GRAPE approach for this problem, we compute gradient of various objectives for general N-level open quantum systems both for piecewise class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a matrix determining the system's dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano's method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated.
arXiv commentThis is the version of the article before peer review or editing, as submitted by an author to Journal of Physics A: Mathematical and Theoretical, with some minor changes. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/ace13f
References in corpus (63)
- Non-Markovian dynamics in open quantum systems
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- Control of quantum phenomena: Past, present, and future
- A Rydberg Quantum Simulator
- Quantum control theory and applications: A survey
- Chopped random-basis quantum optimization
- Controlling open quantum systems: Tools, achievements, and limitations
- Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
- Quantum harmonic oscillator state synthesis by reservoir engineering
- Engineered Dissipation for Quantum Information Science
- Driving at the quantum speed limit: Optimal control of a two-level system
- Monotonically convergent optimization in quantum control using Krotov's method
- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
- Experimental multiparticle entanglement dynamics induced by decoherence
- Singular extremals for the time-optimal control of dissipative spin 1/2 particles
- Quantum memories based on engineered dissipation
- Experimental Machine Learning of Quantum States
- Optimal control of open quantum systems: cooperative effects of driving and dissipation
- Quantum control by von Neumann measurements
- Teaching the Environment to Control Quantum Systems
- Machine learning non-Markovian quantum dynamics
- Alternative fidelity measure for quantum states
- Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
- Controllability of open quantum systems with Kraus-map dynamics
- Robust quantum gates for systems subject to decoherence via optimal control: Markovian vs non-Markovian dynamics
- Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations
- Dissipative quantum control of a spin chain
- Quantum Computer with Mixed States and Four-Valued Logic
- Engineering arbitrary pure and mixed quantum states
- Control landscapes for two-level open quantum systems
- Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered
- Robust Quantum Control in Games: an Adversarial Learning Approach
- Krotov Method for Optimal Control in Closed Quantum Systems
- Quantum state control of a Bose-Einstein condensate in an optical lattice
- Observation-assisted optimal control of quantum dynamics
- Gradient Flows for Optimisation and Quantum Control: Foundations and Applications
- An Efficient Quantum Jump Method for Coherent Energy Transfer Dynamics in Photosynthetic Systems under the Influence of Laser Fields
- Trap-free manipulation in the Landau-Zener system
- Measurement-assisted Landau-Zener transitions
- Gradient Ascent Pulse Engineering with Feedback
- Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
- QuOCS: The Quantum Optimal Control Suite
- Characterization of control noise effects in optimal quantum unitary dynamics
- Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates
- Hessian-based optimization of constrained quantum control
- Reachable sets for two-level open quantum systems driven by coherent and incoherent controls
- Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array
- Nonequilibrium control of thermal and mechanical changes in a levitated system
- Quantum Optimal Control via Semi-Automatic Differentiation
- Unified analysis of terminal-time control in classical and quantum systems
- General unifying features of controlled quantum phenomena
- Bath engineering of a fluorescing artificial atom with a photonic crystal
- Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls
- Pointer States via Engineered Dissipation
- Pontryagin-Optimal Control of a non-Hermitian Qubit
- Constructing grids for molecular quantum dynamics using an autoencoder
- Improved Quantum Computing with the Higher-order Trotter Decomposition
- Energy control in a quantum oscillator using coherent control and engineered environment
- Quantum State Preparation by Controlled Dissipation in Finite Time: From Classical to Quantum Controllers
- Optimization of Controlled-Z Gate with Data-Driven Gradient Ascent Pulse Engineering in a Superconducting Qubit System
- Statistically Characterising Robustness and Fidelity of Quantum Controls and Quantum Control Algorithms
- Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach
- Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search
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- Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
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- Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
- Mitigating controller noise in quantum gates using optimal control theory
- Quantum control landscape for generation of and gates in an open qubit with both coherent and environmental drive
- Gradient projection method for constrained quantum control
- Optimal remote restoring of quantum states in communication lines via local magnetic field
- State preparation of lattice field theories using quantum optimal control
- Unifying methods for optimal control in non-Markovian quantum systems via process tensors
- Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives
- Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
- Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization
- Incoherent GRAPE (inGRAPE) for optimization of quantum systems with environmentally assisted control
- Experimental quantum state transfer of an arbitrary single-qubit state on a cycle with four vertices using a coined quantum random walk
- Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian
- Two-level control over quantum state creation via entangled equal-probability state
- Amplification of quantum transfer and quantum ratchet
- Quantum control by the environment: Turing uncomputability, Optimization over Stiefel manifolds, Reachable sets, and Incoherent GRAPE
- Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System
- Unique determination and generation of rank two single-qubit quantum channels
- Coherence restoring in communication line via controlled interaction with environment