  In this paper we investigate a linear chain of qubits and determine that it
can be configured into a conditional two-qubit swapping gate, where the first
and last qubits of the chain are the swapped qubits, and the remaining middle
ancilla qubits are controlling the state of the gate. The swapping gate
introduces different phases on the final states depending on the initial
states. In particular we focus on a chain of four qubits and show the swapping
gate it implements. We simulate the chain with realistic parameters, and
decoherence noise and leakage to higher excited states, and find an average
fidelity of around 0.99. We propose a superconducting circuit which implements
this chain of qubits and present a circuit design of the circuit. We also
discuss how to operate the superconducting circuit such that the state of the
gate can be controlled. Lastly, we discuss how the circuit can be
straightforwardly altered and may be used to simulate Hamiltonians with
non-trivial topological properties.
