Searching for quantum optimal controls under severe constraints

Abstract

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.

16 pages, 7 figures

References in corpus (69)

• Control of quantum phenomena: Past, present, and future
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Time Optimal Control in Spin Systems
• Shaped-pulse optimisation of coherent soft-x-rays
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Optimal control technique for Many Body Quantum Systems dynamics
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Optimal control theory for unitary transformations
• Quantum Computation with Vibrationally Excited Molecules
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Coherent control using adaptive learning algorithms
• Quantum Control Landscapes
• Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
• Optimal control of a qubit coupled to a non-Markovian environment
• Optimal control, geometry, and quantum computing
• Robust optimal quantum gates for Josephson charge qubits
• Optimal quantum control of Bose Einstein condensates in magnetic microtraps
• Time Optimal Unitary Operations
• Optimal Control for Generating Quantum Gates in Open Dissipative Systems
• Quantum control and measurement of atomic spins in polarization spectroscopy
• Are there traps in quantum control landscapes?
• Robust control of quantum gates via sequential convex programming
• Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles
• Controlling the Dynamics of Many-Electron Systems from First Principles: A Marriage of Optimal Control and Time-Dependent Density-Functional Theory
• Optimal control of entangling operations for trapped ion quantum computing
• Degrees of controllability for quantum systems and applications to atomic systems
• Robust quantum gates for systems subject to decoherence via optimal control: Markovian vs non-Markovian dynamics
• Protecting coherence in Optimal Control Theory: State dependent constraint approach
• Speeding up critical system dynamics through optimized evolution
• Exploring constrained quantum control landscapes
• Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field
• Optimal control of a leaking qubit
• Montonic convergent optimal control theory to modulate bandwidth limited laser pulses in linear and non-linear optical processes
• Implementation of Quantum Logic Gates Using Polar Molecules in Pendular States
• Quantum Control Landscapes: A Closer Look
• Optimal control of number squeezing in trapped Bose-Einstein condensates
• Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations
• Optimal control of atom transport for quantum gates in optical lattices
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Singularities of Quantum Control Landscapes
• Control landscapes for two-level open quantum systems
• Search complexity and resource scaling for the quantum optimal control of unitary transformations
• Characterization of the Critical Submanifolds in Quantum Ensemble Control Landscapes
• Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling
• Coherent open-loop optimal control of light-harvesting dynamics
• Tailoring laser pulses with spectral and fluence constraints using optimal control theory
• Environment-invariant measure of distance between evolutions of an open quantum system
• Criteria for reachability of quantum states
• Steering the optimization pathway in the control landscape using constraints
• Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution
• Control of inhomogeneous atomic ensembles of hyperfine qudits
• Optimized single-qubit gates for Josephson phase qubits
• Quantum control landscape for a $\Lambda$-atom in the vicinity of second order traps
• Characterization of control noise effects in optimal quantum unitary dynamics
• Exploring adiabatic quantum trajectories via optimal control
• Implementation of Quantum Gates via Optimal Control
• Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
• Searching for quantum optimal controls in the presence of singular critical points
• Comment on "Are There Traps in Quantum Control Landscapes?"
• Optimization Schemes for Selective Molecular Cleavage with Tailored Ultrashort Laser Pulses
• Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• The role of controllability in optimizing quantum dynamics
• General unifying features of controlled quantum phenomena
• Time complexity and gate complexity
• Optimal control of the silicon-based donor electron spin quantum computing
• The Optimal Control Landscape for the Generation of Unitary Transformations with Constrained Dynamics
• Coherent control of atomic transport in spinor optical lattices
• Optimal Control of the Electronic Current Density - An application to one- and two-dimensional one-electron systems

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• One decade of quantum optimal control in the chopped random basis
• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• Achieving robust and high-fidelity quantum control via spectral phase optimization
• Quantum Optimal Control for Mixed State Squeezing in Cavity Optomechanics
• Learning Unitaries by Gradient Descent
• Searching for quantum optimal controls in the presence of singular critical points
• Predicting quantum dynamical cost landscapes with deep learning
• Dynamically Correcting a CNOT Gate for any Systematic Logical Error
• Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch
• Searching for an optimal control in the presence of saddles on the quantum mechanical observable landscape
• Parameterized Hamiltonian simulation using quantum optimal control
• Optimal solutions to quantum annealing using two independent control functions