Hamiltonian engineering via invariants and dynamical algebra

Abstract

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than slow, adiabatic ones. As application examples we design families of shortcut Hamiltonians that drive two and a three-level systems between initial and final configurations imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.

References in corpus (13)

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• Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
• Optimal quantum control of Bose Einstein condensates in magnetic microtraps
• Fast ground-state cooling of mechanical resonator with time-dependent optical cavities
• Optimal transport of ultracold atoms in the non-adiabatic regime
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Cited by in corpus (52)

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• Shortcuts to adiabaticity in three-level systems using Lie transforms
• Fast quasi-adiabatic dynamics
• Fast preparation of W states with superconducting quantum interference devices by using dressed states
• Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
• Shortcuts to adiabaticity using flow fields
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Shortcuts to adiabatic passage for fast generation of Greenberger-Horne-Zeilinger states by transitionless quantum driving
• Fast adiabatic evolution by oscillating initial Hamiltonians
• Fast quantum state engineering via universal SU(2) transformation
• Robust and highly-efficient discrimination of chiral molecules through three-mode parallel paths
• Noise Resistant Quantum Control Using Dynamical Invariants
• Shortcuts to Adiabaticity in Krylov Space
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• Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade
• Shortcuts to adiabaticity: Suppression of pair production in driven Dirac dynamics
• Optimal shortcut approach based on an easily obtained intermediate Hamiltonian
• Hamiltonian design to prepare arbitrary states of four-level systems
• Complete Bell-state analysis for superconducting-quantum-interference-device qubits with transitionless tracking algorithm
• Non-Hermitian tight-binding network engineering
• Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system
• Engineered Swift Equilibration for Brownian objects: from underdamped to overdamped dynamics
• Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
• Shaken not stirred: Creating exotic angular momentum states by shaking an optical lattice
• Transitionless-based shortcuts for the fast and robust generation of W states
• Fast driving between arbitrary states of a quantum particle by trap deformation
• Invariant-based inverse engineering of crane control parameters
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Shortcuts in stochastic systems and control of biophysical processes
• Shortcuts to adiabaticity with general two-level non-Hermitian systems
• Counter-diabatic driving for fast spin control in a two-electron double quantum dot
• Speeding up adiabatic passage with an optimal modified Roland-Cerf protocol
• Shortcut to adiabaticity in a Stern-Gerlach apparatus
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals
• Invariant-based pulse design for three-level systems without the rotating-wave approximation
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
• The Dynamical Invariant of Open Quantum System
• Accelerating population transfer in a transmon qutrit via Shortcuts to adiabaticity
• Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering
• Shortcut to stationary regimes: a simple experimental demonstration
• Shortcuts to thermodynamic quasistaticity
• Accelerating adiabatic quantum transfer for three-level $\Lambda$-type structure systems via picture transformation
• Dynamical invariant formalism of shortcuts to adiabaticity
• Quantum control without quantum states
• Robust implicit quantum control of interacting spin chains
• Engineered Robustness for Nonadiabatic Geometric Quantum Gates
• Lie transformation on shortcut to adiabaticity in parametric driving quantum system
• Environment-Assisted Shortcuts to Adiabaticity