Dynamical invariants for quantum control of four-level systems

Abstract

We present a Lie-algebraic classification and detailed construction of the dynamical invariants, also known as Lewis-Riesenfeld invariants, of the four-level systems including two-qubit systems which are most relevant and sufficiently general for quantum control and computation. These invariants not only solve the time-dependent Schrödinger equation of four-level systems exactly but also enable the control, and hence quantum computation based on which, of four-level systems fast and beyond adiabatic regimes.

11 pages, 5 tables

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• Fast and robust creation of an arbitrary single qubit state by nonadiabatic shortcut pulses in a three-level system
• The driven-Markovian master equation based on the Lewis-Riesenfeld invariants theory
• Dropout is all you need: robust two-qubit gate with reinforcement learning
• Nonadiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition
• Dynamical invariant formalism of shortcuts to adiabaticity
• Dynamics of a driven open double two-level system and its entanglement generation
• Dynamical invariants and quantization of the one-dimensional time-dependent, damped, and driven harmonic oscillator
• Engineered Robustness for Nonadiabatic Geometric Quantum Gates