  We have synthesized the anti-symmetric spin exchange interaction (ASI), which
is also called the Dzyaloshinskii-Moriya interaction, in a superconducting
circuit containing five superconducting qubits connected to a bus resonator, by
periodically modulating the transition frequencies of the qubits with different
modulation phases. This allows us to show the chiral spin dynamics in three-,
four- and five-spin clusters. We also demonstrate a three-spin chiral logic
gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our
results pave the way for quantum simulation of magnetism with ASI and quantum
computation with chiral spin states.
