Geometric quantum speed limits and short-time accessibility to unitary operations
arXiv:1901.02042 · doi:10.1103/PhysRevA.99.042116
Abstract
The notion of quantum speed limit (QSL) refers to the fundamental fact that two quantum states become completely distinguishable upon dynamical evolution only after a finite amount time, called the QSL time. A different, but related concept is that of minimum control time (MCT), which is the minimum evolution time needed for a state to be driven (by suitable, generally time-dependent, control fields) to a given target state. While the QSL can give information about the MCT, it usually imposes little restrictions to it, and is thus unpractical for control purposes. In this work we revisit this issue by first presenting a theory of geometrical QSL for unitary transformations, rather than for states, and discuss its implications and limitations. Then, we propose a framework for bounding the MCT for realizing unitary transformations that goes beyond the QSL results and gives much more meaningful information to understand the controlled dynamics of the system at short times.
arXiv comment11 pages, 5 figures
References in corpus (39)
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Training Schrödinger's cat: quantum optimal control
- A programmable two-qubit quantum processor in silicon
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Quantum Computation as Geometry
- Experimental Comparison of Two Quantum Computing Architectures
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Optimal Control at the Quantum Speed Limit
- Quantum speed limits in open system dynamics
- Optimal control technique for Many Body Quantum Systems dynamics
- Quantum limits to dynamical evolution
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Statistical distinguishability between unitary operations
- Generalized Geometric Quantum Speed Limits
- Coherent many-body spin dynamics in a long-range interacting Ising chain
- Implementing optimal control pulse shaping for improved single-qubit gates
- Energy-time uncertainty relation for driven quantum systems
- Quantum Speed Limits Across the Quantum-to-Classical Transition
- Quantum Speed Limit is Not Quantum
- Towards quantum simulation with circular Rydberg atoms
- Time Optimal Unitary Operations
- High-fidelity Rydberg quantum gate via a two-atom dark state
- Optimal control methods for fast time-varying Hamiltonians
- Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
- Exploring the Quantum Speed Limit with Computer Games
- Speeding up critical system dynamics through optimized evolution
- Zermelo Navigation and a Speed Limit to Quantum Information Processing
- Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations
- Quantum Speed Limit and optimal evolution time in a two-level system
- Optimized controlled Z gates for two superconducting qubits coupled through a resonator
- The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms
- Solution to the quantum Zermelo navigation problem
- Time-optimal synthesis of SU(2) transformations for a spin-1/2 system
- Zermelo Navigation in the Quantum Brachistochrone
- Quantum Optimal Control: Landscape Structure and Topology
- The roles of drift and control field constraints upon quantum control speed limits
- Relation Between Quantum Speed Limits And Metrics On U(n)
- Enhancement of quantum speed limit time due to cooperative effects in multilevel systems
Cited by in corpus (22)
- Action quantum speed limits
- Energetic cost of quantum control protocols
- Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
- Quantum speed limits on operator flows and correlation functions
- Operational definition of a quantum speed limit
- From quantum speed limits to energy-efficient quantum gates
- Universally Robust Quantum Control
- Diverging quantum speed limits: a herald of classicality
- Shortcuts to Dynamic Polarization
- Quantum speed limit for robust state characterization and engineering
- Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
- Bhatia-Davis formula in the quantum speed limit
- Ultrafast critical ground state preparation via bang-bang protocols
- Analysis of lower bounds for quantum control times and their relation to the quantum speed limit
- Quantum speed limit of Jaynes-Cummings model with detuning for arbitrary initial states
- Enhancing precision thermometry with nonlinear qubits
- Reachable Set Characterization of Open Quantum System by Quantum Speed Limit
- Quantum speed limit of a single atom in a squeezed optical cavity mode
- Quantum speed limits in dephasing dynamics of a qubit system coupled to thermal environments
- Quantum Speed Limits from Symmetries in Quantum Control
- Nonlinear speed-ups in ultracold quantum gases
- High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach