Necessary and sufficient condition for quantum adiabatic evolution by unitary control fields

Abstract

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.

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• Generalized Adiabatic Theorems: Quantum Systems Driven by Modulated Time-Varying Fields
• Tuning the initial phase to control the final state of a driven qubit
• Two-photon-transition superadiabatic passage in an nitrogen-vacancy center in diamond
• A necessary condition for quantum adiabaticity applied to the adiabatic Grover search
• Robust transitionless quantum driving: Concatenated approach
• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Robust Coherent Superposition of States using Quasiadiabatic Inverse Engineering
• Accelerating quantum adiabatic evolution with $\pi$-pulse sequences
• Geometric Floquet Condition for Quantum Adiabaticity
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Speeding up adiabatic holonomic quantum gates via $\pi$-pulse modulation