The implementation of holonomic quantum computation generally requires controllable and complicated interaction among addressable multi-level systems, which is challenging on superconductingcircuit. Here, we propose a scalable architecture for non-adiabatic holonomic quantum computation on a circuit QED lattice with hybrid transmon and photon encoding of the logical qubits in a decoherence-free subspace. With proper driven on the transmon, we can obtain tunable resonate interaction between the transmon and each of the resonators, which leads to arbitrary single-qubit operation on the encoded logical qubit. Meanwhile, for a nontrivial two-qubit gate, we only need resonate interactions among the three resonators from the two logical qubits, which can be induced by commonly coupled to a grounding SQUID with ac magnetic driven. More importantly, our scheme is achieved with all resonate interactions among the involved elements, and thus leads to quantum gates with very high fidelity. Therefore, our scheme opens up the possibility of realizing high fidelity universal holonomic quantum computation in solid-state system.
We propose to implement tunable interaction of superconducting flux qubits with cavity-assisted interaction and strong driving. The qubits have a three-level Lambda configuration, andthe decay of the excited state will be greatly suppressed due to the effective large detuning. The implemented interaction is insensitive to the cavity field state and can be controlled by modulating the phase difference of the driving fields of the qubits. In particular, our scheme is based on the typical circuit QED setup and thus will provide a simple method towards the tunable interaction of superconducting qubits. Finally, we consider the generation of two and four qubits entangled states with the constructed interaction under the influence of typical decoherence effects.
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that thecoupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work opens up the possibility of studying quantum nonlinear effect in circuit electromechanics.
To implement a universal set of quantum logic gates based on non-Abelian geometric phases, one needs quantum systems that are beyond two levels. However, this is extremely difficultfor superconducting qubits, and thus the recent experiment has only realized single qubit gates [A. A. Abdumalikov Jr et al., Nature 496, 482 (2013)]. Here, we propose to implement non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where we only use two levels in transmon qubits, and require minimal resources for the decoherence-free subspace encoding. In this way, our scheme avoids difficulties in previous works while still can achieve considerable large effective coupling strength and thus leads to high fidelity quantum gates. Therefore, our scheme presents a promising way for robust quantum computation on superconducting circuits.
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.