Time-optimal control of a dissipative qubit
arXiv:2002.07653 · doi:10.1103/PhysRevA.101.022320
Abstract
A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with bounded amplitude. The coupling between the bath and the qubit is modeled by a Lindblad master equation. Dissipation typically drives the system to the maximally mixed state; consequently, there generally exists an optimal evolution time beyond which the decoherence prevents the system from getting closer to the target state. For some specific dissipation channel, however, the optimal control can keep the system from the maximum entropy state for infinitely long. The conditions under which this specific situation arises are discussed in detail. The numerical procedure to construct the time-optimal protocol is described. In particular, the formalism adopted here can efficiently evaluate the time-dependent singular control which turns out to be crucial in controlling either an isolated or a dissipative qubit.
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References in corpus (30)
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- A variational eigenvalue solver on a quantum processor
- Quantum Mechanics helps in searching for a needle in a haystack
- Advances in Quantum Metrology
- Quantum information with continuous variables
- Gaussian Quantum Information
- Quantum metrology
- Quantum Annealing in the Transverse Ising Model
- Free-Space distribution of entanglement and single photons over 144 km
- Shortcuts to adiabaticity: concepts, methods, and applications
- A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application
- Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
- Scalable Quantum Simulation of Molecular Energies
- Quantum Annealing and Analog Quantum Computation
- Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
- Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
- Electronic properties and metrology of the diamond NV- center under pressure
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Dense Coding for Continuous Variables
- Observation of Entangled States of a Fully Controlled 20-Qubit System
- Reinforcement Learning in Different Phases of Quantum Control
- Fast-forward of adiabatic dynamics in quantum mechanics
- Driving at the quantum speed limit: Optimal control of a two-level system
- A scalable control system for a superconducting adiabatic quantum optimization processor
- Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
- Geometric Speed Limit of Accessible Many-Body State Preparation
- High-Speed Driving of a Two-Level System
- Fast adiabatic evolution by oscillating initial Hamiltonians
- Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: preparing a maximally entangled state with singular bang-bang protocols
- Application of Pontryagin's Minimum Principle to Grover's Quantum Search Problem
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