Dynamical invariants for quantum control of four-level systems

TL;DR

This paper develops a Lie-algebraic framework for constructing dynamical invariants in four-level quantum systems, enabling exact solutions and advanced quantum control beyond adiabatic limits.

Contribution

It provides a detailed classification and construction of Lewis-Riesenfeld invariants for four-level systems, including two-qubit systems, advancing quantum control methods.

Findings

Exact solutions to time-dependent Schrödinger equations for four-level systems

Enabling fast, non-adiabatic quantum control and computation

Framework applicable to two-qubit systems and beyond

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 Schr\"odinger 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.