A general formulation of time-optimal quantum control and optimality of singular protocols
arXiv:2001.00029 · doi:10.1088/1367-2630/ab8ab3
Abstract
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the variational principle, whose drawback is that it deals with equality constraints only. While inequality constraints can be reduced to equality ones in some situations, there are situations where they cannot, especially when a drift field is present in the Hamiltonian. The drift which we cannot control appears in a wide range of systems. We first develop a framework based on Pontryagin's maximum principle (MP) in order to deal with inequality constraints as well. The new framework contains QB as a special case, and their detailed correspondence is given. Second, using this framework, we discuss general relations among the drift, the singular controls, and the inequality constraints. The singular controls are those that satisfy MP trivially so as to cause a trouble in determining the optimal protocol. Third, to overcome this issue, we derive an additional necessary condition for a singular protocol to be optimal by applying the generalized Legendre-Clebsch condition. This condition in particular reveals the physical meaning of singular controls. Finally, we demonstrate how our framework and results work in some examples.
arXiv comment31 pages, 4 figures
References in corpus (49)
- Quantum Computing in the NISQ era and beyond
- Quantum Annealing in the Transverse Ising Model
- Shortcuts to adiabaticity: concepts, methods, and applications
- Control of quantum phenomena: Past, present, and future
- The maximum speed of dynamical evolution
- Training Schrödinger's cat: quantum optimal control
- Time Optimal Control in Spin Systems
- Fast optimal frictionless atom cooling in harmonic traps
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Quantum Computation as Geometry
- Quantacell: Powerful charging of quantum batteries
- A geometric theory of non-local two-qubit operations
- Optimally robust shortcuts to population inversion in two-level quantum systems
- Quantum Brachistochrone
- Fast population transfer engineering of three-level systems
- Driving at the quantum speed limit: Optimal control of a two-level system
- Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
- Singular extremals for the time-optimal control of dissipative spin 1/2 particles
- Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
- Optimal control, geometry, and quantum computing
- Time Optimal Unitary Operations
- Transitionless quantum driving for spin systems
- Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
- Pulsed Laser Cooling for Cavity-Optomechanical Resonators
- Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control
- Time-optimal control of SU(2) quantum operations
- Physical Optimization of Quantum Error Correction Circuits
- Interaction cost of non-local gates
- Zermelo Navigation and a Speed Limit to Quantum Information Processing
- Experimental time-optimal universal control of spin qubits in solids
- Solution to the quantum Zermelo navigation problem
- Time-optimal navigation through quantum wind
- Time-optimal synthesis of SU(2) transformations for a spin-1/2 system
- Time-Optimal Universal Control of Two-Level Systems under Strong Driving
- Quantum Brachistochrone for Mixed States
- Zermelo Navigation in the Quantum Brachistochrone
- Dynamical invariants for quantum control of four-level systems
- Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems
- Geometric Approach to Pontryagin's Maximum Principle
- Shaken not stirred: Creating exotic angular momentum states by shaking an optical lattice
- Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
- Optimal simulation of nonlocal Hamiltonians using local operations and classical communication
- Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
- Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
- Fast Quantum Communication in Linear Networks
- Time complexity and gate complexity
- Spatial non-adiabatic passage using geometric phases
- Landau-Zener tunneling problem for Bloch states
- Brachistochrone of Entanglement for Spin Chains
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- Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
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- Time optimal quantum state transfer in a fully-connected quantum computer