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INFORMATION PROCESSING WITH QUBITS IN A MICROWAVE FIELD

Mohamed R. Abdelhafez, Heba Kadry

Published Aug 1, 2014• 0 citations

Abstract

Recently, great interest has attracted many proposals to build and construct the quantum computer both theoretically and experimentally. The superconducting Josephson junc tions (Cooper-pair box) circuits is one of the most promising hardware architecture for the realization of a scalable quantum computer processor. The production, controlling and manipulation of the quantum bits are still not completely solved. In this thesis we studied the interaction of the multi-photon field with single Cooper-pair box. First, the theoretical model which describes our system is reported. The analytical expression of the reduced density operator of the cavity field and the Cooper-pair is calculated. The dynamical properties of various parameters on the mean number of the Cooper pairs are studied. It is shown that the system parameters play an important role in the dy namics of the qubits in the system.

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Recently, great interest has attracted many proposals to build and construct the quantum computer both theoretically and experimentally. The superconducting Josephson junc tions (Cooper-pair box) circuits is one of the most promising hardware architecture for the realization of a scalable quantum computer processor. The production, controlling and manipulation of the quantum bits are still not completely solved. In this thesis we studied the interaction of the multi-photon field with single Cooper-pair box. First, the theoretical model which describes our system is reported. The analytical expression of the reduced density operator of the cavity field and the Cooper-pair is calculated. The dynamical properties of various parameters on the mean number of the Cooper pairs are studied. It is shown that the system parameters play an important role in the dy namics of the qubits in the system.

The concept of a quantum computer was invented in the beginning of the 1980s as a quantum generalization of the reversible classical computer. After discoveries in the middle of the 1990s of quantum algorithms, which wouldsolve some problems considered intractable for classical computers, the field of quantum computing has developed rapidly. A wide range of quantum systems are investigated for their possible ability to implement quantum algorithms in practice. The most promising solid state implementations are superconducting electrical circuits based on the Josephson effect, and the Coulomb blockade effect. Superconducting circuits are macroscopic quantum systems which can be fabricated using standard lithography technologies. Superconducting qubits - basic building blocks of a quantum computer - have been developed at several research laboratories, among others the MC2 here at Chalmers. This thesis presents a theoretical investigation of controllable coupling of superconducting qubits based on the single Cooper-pair box. Two coupling schemes are investigated in detail: current-controlled coupling via large Josephson junctions, and coupling via a superconducting stripline cavity. Both coupling designs are scalable and suitable for the charge regime of the single Cooper-pair box, as well as for the charge-phase regime where the qubit is better protected from environmental noise. Quantum gate protocols which are relevant for these physical couplings are discussed. The investigations show that, for both considered designs, the simplest two-qubit gate is the conditional phase-shift gate. This gate is universal for quantum computing, and it can create maximallyentangled qubit pairs in only one run. The investigation combines methods from electrical engineering, quantum mechanics and quantum computer science.

A Cooper-pair box biased by a classical voltage and also irradiated by a squeezed state field is considered in order to find new ways to quantum communication and calculation. The quantum dynamics of the Cooper-pair box and the entanglement which is the core theoretics of quantum communication and calculation is investigated in this system, which is related to the squeezing parameter of the squeezed state. A model of Hamiltonian which represents the interaction between box and quantum field is introduced. Finally, the relationship between the entanglement and the squeezing parameter of the squeezed state is demonstrated.