# Time-Optimal Control of Collisional $\sqrt{\text{SWAP}}$ Gates in Ultracold Atomic Systems

## TL;DR

This paper employs quantum optimal control to significantly accelerate collisional two-qubit gates in ultracold atoms, optimizing the entire process rather than individual steps, leading to faster and more reliable quantum gate operations.

## Contribution

It introduces a full-gate optimization approach that surpasses traditional methods by not relying on atoms in lowest eigenstates and incorporating phase accumulation, applicable across various trapping geometries.

## Key findings

- Achieved faster gate durations with higher fidelities.
- Demonstrated the effectiveness of full-gate optimization over stepwise methods.
- Provided systematic results for optical lattice setups.

## Abstract

We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\text{SWAP}}$ gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.