An exotic DIII model of one-dimensional p-wave spin-triplet superconductors with the ℤ2 topological phase protected by the time-reversal symmetry is simulated by an array of inductivelycoupled transmon qubits with tunable nearest-neighbor couplings and scalability. The anti-commutation relation between opposite spin components in the DIII model is realized by a novel dispersive dynamic modulation approach, while previous schemes consider only spinless fermions. Our detailed analysis reveals that distinctive topological phenomena can be visualized with the state-of-the-art technology in this superconducting-circuit array.
We propose a scheme to simulate the 1D Majorana equation with two Cooper pair boxes coupled to a 1D superconducting transmission line resonator, where strong coupling limit can be achieved.With proper chosen of systematic parameters, we are able to engineer different kinds of interaction, which is indispensable in simulating the Majorana equation in an enlarged real Hilbert space. Measurement of the conserved observable of pseudo-helicity via transmission spectrum of the cavity field can verify the simulated Majorana wave function. The measurement results are experimentally resolvable based on our estimation with conservative parameters.
We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits,which can realize arbitrary single-qubit gate on the topological qubit. When two qubits are involved, the interface between the topological qubits and a microwave cavity can induce a nontrivial two-qubit gate, which can not be constructed based on braiding operations. The two interfaces, being tunable via an external magnetic flux, may serve as the building blocks towards universal quantum computation with topological qubits.
We propose a scheme for detecting noncommutative feature of the non-Abelian geometric phase in circuit QED, which involves three transmon qubits capacitively coupled to an one-dimensionaltransmission line resonator. By controlling the external magnetic flux of the transmon qubits, we can obtain an effective tripod interaction of our circuit QED setup. The noncommutative feature of the non-Abelian geometric phase is manifested that for an initial state undergo two specific loops in different order will result in different final states. Our numerical calculations show that this difference can be unambiguously detected in the proposed system.