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We have synthesized the anti-symmetric spin exchange interaction (ASI), whichis also called the Dzyaloshinskii-Moriya interaction, in a superconductingcircuit containing five superconducting qubits connected to a bus resonator, byperiodically modulating the transition frequencies of the qubits with differentmodulation phases. This allows us to show the chiral spin dynamics in three-,four- and five-spin clusters. We also demonstrate a three-spin chiral logicgate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Ourresults pave the way for quantum simulation of magnetism with ASI and quantumcomputation with chiral spin states.

Synthesis of antisymmetric spin exchange interaction and entanglement generation with chiral spin states in a superconducting circuit