Counterdiabatic-influenced Floquet-engineering: State preparation, annealing and learning the adiabatic gauge potential

TL;DR

This paper introduces CAFFEINE, a hybrid quantum control technique that uses Floquet engineering and optimal control to achieve adiabatic state preparation and quantum annealing without explicitly deriving counterdiabatic terms.

Contribution

CAFFEINE parameterizes Floquet Hamiltonians for counterdiabatic driving and employs numerical optimal control, simplifying implementation and enabling learning of counterdiabatic terms.

Findings

Successfully prepared Bell states with two qubits.

Implemented quantum annealing protocols for the 1D Ising model.

Demonstrated learning of counterdiabatic terms as probes of quantum chaos.

Abstract

Counterdiabatic driving, which enforces adiabatic evolution in arbitrary timescales, can be realised by engineering a Floquet Hamiltonian which oscillates between the Hamiltonian and its derivative requiring no additional control terms. However, the coefficients of the Floquet Hamiltoinan require knowledge of the counterdiabatic terms, which can be difficult to derive outside of a limited set of examples. We introduce a new hybrid technique for the control of quantum systems, Counterdiabatic-influenced Floquet-engineering or CAFFEINE for short. CAFFEINE parameterises the Floquet Hamiltonian for counterdiabatic driving and utilises numerical quantum optimal control in order to obtain the desired target state. This removes the need to both obtain and implement counterdiabatic terms, however, it does require the ability to quickly oscillate each term in the Hamiltonian. If this oscillation is possible, then CAFFEINE provides a framework to implement quantum annealing protocols and general quantum state preparation. We illustrate this through optimisation of two numerical examples of preparing a Bell state with two qubits and performing annealing protocols for the one-dimensional Ising model. Beyond this, we also illustrate CAFFEINE's capabilities to learn the counterdiabatic terms, which can potentially be used as a probe of quantum chaos and the geometry of quantum dynamics.