Efficient generation of the triplet Bell state between coupled spins using transitionless quantum driving and optimal control

Abstract

We consider a pair of coupled spins with Ising interaction in z-direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large become the available control fields. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. The results of the present work are not restricted only to spin systems, but is expected to find also applications in other physical systems which can be modeled as interacting spins, such as, for example, coupled quantum dots.

Energetic cost of quantum control protocols

“…There is complete freedom in both the form of the ramp and its duration. Turning to LCD, perfect target state fidelity can be achieved by making a unitary transformation of H 0 +H CD to arrive at [14,52] s…”

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

“…Optimal control provides a powerful tool to solve time-optimal and energy-optimal problems in quantum two-level and three-level systems [ 70 , 71 , 72 , 73 ]. Such result can be directly extended to two uncoupled [ 72 ] and coupled [ 74 ] spins with similar approach. Using numerical optimal algorithm, robust optimal control can also be designed that accounts for inhomogeneous boarding and/or dissipation [ 71 , 75 , 76 , 77 ].…”

Finite-time two-spin quantum Otto engines: Shortcuts to adiabaticity vs. irreversibility

“…H CD (t = 0, τ ) = 0 so that our system is described by its original Hamiltonian at these points. It is possible to ensure this by assuming various polynomial forms for the driven system parameter [29,31,35,36,49,50] depending on the desired smoothness of the driving. However, we have not seen any significant difference between them for our purposes in this work, and therefore continue with the simple choice below which ensures continuous first time derivatives at the boundaries…”