Study Of Superconducting Quantum Computation Based On Josephson Junctions

Because of their excellent scalability, superconducting quantum circuits are regardedas very potential candidates for implementing quantum computation. At present,superconducting quantum computation is facing a big difficulty, i.e. superconductingqubits have very short coherence times, which makes superconducting quantumcomputers difficult to implement a practical task of quantum information processing. Tocomplete more operations in the coherence times, we must improve the existingcomputation protocols, e.g. constructing faster logic gates, designing new computationprotocols better than the standard gate-decomposition protocol and so on. This thesismainly focuses on the new quantum computation protocols based on superconductingsystems. Besides, we explore the applications of superconducting quantum circuits inquantum simulation. The main results and the creative points are as follows.We propose a theoretical protocol for the fast quantum phase gate in a circuit QEDmodel. In our protocol, two charge qubits are capacitively coupled to a superconductingtransmission line resonator driven by a strong microwave field. It is shown that undercertain conditions, the qubit-resonator interaction parts in the evolution operator arecanceled and an XX-type operator between two separate qubits can be achieved. Basedon this XX-type interaction, we can implement the quantum phase gate between thequbits easily. Compared with previous protocols, our protocol works at a small detuningand the nontrivial two-qubit gate is almost one order of magnitude faster than theprevious ones. Furthermore, via setting the system parameters appropriately, we canrealize the general conditional phase shift gate of the charge qubits, which is very usefulfor implementing the large-scale quantum Fourier transform algorithm.We present a potential scheme to implement one-way quantum computation usingcharge qubits as information carriers. In our scheme, a superconducting transmissionline resonator is driven by a strong microwave field, and N identical charge qubits arefabricated at the antinodes of the electric field of the (N1) thresonator mode. Usingthe resonator as an auxiliary system, we can derive the controllable Ising interaction ofthose charge qubits. Based on the controllable Ising interaction, one-dimentional largecluster states of charge qubits can be generated in just one step. A single-qubitmeasurement in the arbitrary basis can be implemented using a single electron transistorwith the help of one-qubit rotations. This scheme has the advantages of simple clusterstate generation, little time consumtion and slight influence from the main decoherencesources.We propose a scalable architecture for one-way quantum computation usingmicrowave photons in the coupled networks of resonators as information carriers. In our protocol, quantum information is encoded into the lowest two Fock states of the high-Qtransmission line resonators. Each resonator in our architecture contains a charge qubitinside it, which is used for the state initialization and local projective measurement ofthe photonic qubit. Any pair of neighboring photonic qubits are coupled via a mediatorcharge qubit fabricated between the resonators. Large photonic cluster states can becreated in2d steps by applying a series of Rabi pulses to the charge qubits at theresonator junctions, where d is the dimension of the resonator lattice. Thanks to theflexibility of the connections between the resonators fabricated on a chip, we can obtainarbitrary dimensional cluster states in principle. The distinct advantage of ourarchitecture is that it combines both the excellent scalability of the solid-state systemsand the long coherence time of the photonic qubits.We give a concrete experimental scheme for simulating Bose-Hubbard model usingmicrowave photons in the coupled networks of superconducting resonators. In ourproposed architecture, microwave photons play the roles of bosons, the strongqubit-photon coupling inside the resonator leads to an effective polariton repulsion, andthe adjacent resonators are coupled by another dispersive charge qubit playing the roleof an effective knob for the photon hopping rate. The advantage of this scheme is thatthe on-site repulsion and the photon-hopping rate can be tuned independently, which isdesirable for observing the quantum phase transition from the photonic superfluid phaseto the Mott insulator phase. Our numerical analysis shows that, with a small sizeone-dimensional resonator array, we may observe the main characters of Bose-Hubbardmodel experimentally.In addition to simulating some many-body physical models, the resonator array canalso be used for engineering novel quantum states. We propose a method to coherentlysuperpose the insulator and superfluid phases of photons in a2-site resonator array. Inour model, two nonlinear superconducting stripline resonators are coupled by aninterfacial circuit composed of parallel combination of a superconducting qubit and acapacitor. It is shown that the photon hopping rate of the adjacent resonators is stronglydependent on the quantum state of the mediator qubit. With the qubit in itsground/excited state, the adjacent resonators are decoupled/strongly coupled. Byapplying a microwave field with appropriate frequency on the mediator qubit, we coulddemonstrate Rabi oscillation between photonic insulator phase and superfluid phase.Furthermore, this set-up is a promising candidate for implementing distributed quantumcomputation since it is capable of coupling remote qubits in separate resonators in acontrollable way.