Simulation of anyonic fractional statistics of Kitaev's toric model in circuit QED

Since the anyonic excitations in the Kitaev toric model are perfectly localized quasiparticles, it is possible to generate dynamically the ground state and the excitations of the model Hamiltonian to simulate the anyonic interferometry. We propose a scheme in circuit QED to simulate the interferometry. The qubit-cavity interaction can be engineered to realize effective state control as well as the controlled dynamics of qubits, which are sufficient to prepare the ground states, create and remove the anyonic excitation, and simulate the anyonic interferometry. The simplicity and high fidelity of the operations used open the very promising possibility of simulating fractional statistics of anyons in a macroscopic material in the near future.Comment: Typos correcte

Simple unconventional geometric scenario of one-way quantum computation with superconducting qubits inside a cavity

We propose a simple unconventional geometric scenario to achieve a kind of nontrivial multi-qubit operations with superconducting charge qubits placed in a microwave cavity. The proposed quantum operations are insensitive not only to the thermal state of cavity mode but also to certain random operation errors, and thus may lead to high-fidelity quantum information processing. Executing the designated quantum operations, a class of highly entangled cluster states may be generated efficiently in the present scalable solid-state system, enabling one to achieve one-way quantum computation.Comment: Accepted version with minor amendments. To appear in Phys. Rev.

Detecting fractional Josephson effect through 4π4\pi phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe fractional DC Josephson effect of semiconductor nanowire-based topological Josephson junction through 4{\pi} phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting the resonant tunneling with 4{\pi} phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4{\pi} phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.Comment: 5 pages, 3 figure

Detecting fractional Josephson effect through 4π4\pi phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe fractional DC Josephson effect of semiconductor nanowire-based topological Josephson junction through 4{\pi} phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting the resonant tunneling with 4{\pi} phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4{\pi} phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.Comment: 5 pages, 3 figure

Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits

To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is a conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfil for superconducting qubits, appearing to be a main reason why only single qubit gates was implemented in a recent experiment [A. A. Abdumalikov Jr \emph{et al}., Nature 496, 482 (2013)]. Here we propose to realize non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies, but also can still achieve considerably large effective coupling strength, such that high fidelity quantum gates can be achieved. Therefore, the present scheme makes it very promising way to realize robust holonomic quantum computation with superconducting circuits.Comment: V4: published version; V1: submitted on April