Quantum computation attaches importance to high-precision quantum manipulation, where the quantum state transfer with high fidelity is necessary. Here, we propose a new scheme to implementthe quantum state transfer of high fidelity and long distance, by adding on-site potential into the qubit chain and enlarging the proportion of the coupling strength between the two ends and the chain. In the numerical simulation, without decoherence, the transfer fidelities of 9 and 11 qubit chain are 0.999 and 0.997, respectively. Moreover, we give a detailed physical realization scheme of the quantum state transfer in superconducting circuits, and discuss the tolerance of our proposal against decoherence. Therefore, our scheme will shed light on quantum computation with long chain and high-fidelity quantum state transfer.
In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states has attracted much attention recently. However,due to the operational difficulties in solid state materials, non-Abelian statistics has not been experimentally realized yet. The superconducting quantum circuits system is scalable and controllable, thus is a promising platform for quantum simulation. Here, we propose a scheme to demonstrate non-Abelian statistics of topologically protected zero energy edge modes on a chain of the superconducting circuits. Specifically, we can realize topological phase transition by varying the hopping strength and magnetic filed in the chain, and the realized non-Abelian operation can be used in topological quantum computation. Considering the advantages of the superconducting quantum circuits, our protocol may shed light on quantum computation via topologically-protected states.
Topological states of quantum matter %, originally discovered and investigated in condensed matter physics, have inspired both fascinating physics findings and exciting opportunitiesfor applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum simulation of topological matter is very important in deepening our understanding of these states. This requirement puts the quantum superconducting circuits system as a good option for mimicking topological materials, owing to their flexible tunability and fine controllability. As a typical example herein, we realize a Z2-type topological insulator featuring the quantum spin Hall effect state, using a coupled system of transmission-line resonators and transmons. The single-excitation eigenstates of each unit cell are used as a pseudo-spin 1/2 system. Time reversal symmetry of the system is proved, and the boundary of the topological phase transition is fixed in the phase diagram. Topological edge states are shown, which can be experimentally verified by detecting the population at the boundary of the plane. Compared to the previous simulations, this compositional system is fairly controllable, stable and less limited. Therefore, our scheme provides a reliable platform for faithful quantum simulations of topological matter.