Splitting and connecting singlets in atomic quantum circuits

Gate operations composed in quantum circuits form the basis for digital quantum simulation and quantum processing. While two-qubit gates generally operate on nearest neighbours, many circuits require nonlocal connectivity and necessitate some form of quantum information transport. Yet, connecting distant nodes of a quantum processor still remains challenging, particularly for neutral atoms in optical lattices. Here, we create singlet pairs of two magnetic states of fermionic potassium-40 atoms in an optical lattice and use a bi-directional topological Thouless pump to transport, coherently split, and separate the pairs, as well as to demonstrate interaction between them via tuneable $($swap$)^\alpha$-gate operations. We achieve pumping with a single-shift fidelity of 99.78(3)% over 50 lattice sites and split the pairs within a decoherence-free subspace. Gates are implemented by superexchange interaction, allowing us to produce interwoven atomic singlets. For read-out, we apply a magnetic field gradient, resulting in single- and multi-frequency singlet-triplet oscillations. Our work shows avenues to create complex patterns of entanglement and new approaches to quantum processing, sensing, and atom interferometry.