Theoretical investigation of coupled superconducting qubits

A. J. Berkley, S. A. Govorkov, M. C. Thom +1 more

Alexander Shnirman

Margareta Wallquist

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.

Ari Mizel

In the design and investigation of superconducting qubits and related devices, a lumped-element circuit model is the standard theoretical approach. However, many important physical questions lie beyond its scope, such as the behavior of circuits with strong Josephson junctions carrying substantial currents and the properties of very small superconducting devices. By performing gauge transformations on self-consistent solutions of the Bogoliubov--de Gennes equations, we develop here a formalism that treats Josephson couplings nonperturbatively. We apply the formalism to (a) show that Fermi sea effects can contribute to the effective capacitance of small charge qubits; (b) demonstrate an asymmetry in clockwise and counterclockwise current states in small rf superconducting quantum interference device qubits; and (c) provide a microscopic wave function of superconducting Schr\"odinger cats suitable for computing the number of entangled electrons.

Lihua Wang

In Born-Markov approximation,according to Bloch-Redfield equation,the method to calculate the relaxation time T1 and decoherence time T2 of superconducting qubit is given.Based on this,the decoherence phenomenon of superconducting flux qubit with mutual inductance coupling is investigated.The energy relaxation time T1 and decoherence time T2 of this superconducting qubit is also obtained.The results show that for the flux qubit under investigation,the dephasing time T,the energy relaxation time T1 from high level |j〉 to low level |i〉,and the decoherence time T2 of the quantum system are all proportional to dissipation when other conditions are invariant and the environment thermal bath is equivalent to a pure resistance.

Kouichi Semba