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arXiv:quant-ph/9905043 · Physical Review A

Operation of universal gates in a solid-state quantum computer based on clean Josephson junctions betweend-wave superconductors

Alexandre Blais, Alexandre M. Zagoskin

Published Mar 16, 2000• 89 citations
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Abstract

The operation of a solid-state superconducting quantum computer based on clean Josephson junctions between two d-wave superconductors is considered. We show that freezing of passive qubits can be achieved using a dynamic global refocusing technique. Further, we demonstrate that a universal set of gates can be realized on this system, thereby proving its universality.

DOI
10.1103/physreva.61.042308

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The operation of a solid-state superconducting quantum computer based on clean Josephson junctions between two d-wave superconductors is considered. We show that freezing of passive qubits can be achieved using a dynamic global refocusing technique. Further, we demonstrate that a universal set of gates can be realized on this system, thereby proving its universality.
The technologies of Josephson-junction-based qubits have been progressing rapidly, ever since its first demonstration by a superconducting charge qubit1. A variety of systems have been implemented with remarkable progress in coherence time and read-out schemes. Although the current level of this solid-state device is still not as advanced as that of the most advanced microscopic-system-based qubits, these developments, together with the potential scalability, have renewed its position as a strong candidate as a building block for the quantum computer. Recently, coherent oscillation and microwave spectroscopy in capacitively-coupled superconducting qubits have been reported. The next challenging step toward quantum computation is a realization of logic gates. Here we demonstrate a conditional gate operation using a pair of coupled superconducting charge qubits. Using a pulse technique, we prepare different input states and show that they can be transformed by controlled-NOT (C-NOT) gate operation in the amplitude of the states. Although the phase evolution during the gate operation is still to be clarified, the present results are a major step toward the realization of a universal solid-state quantum gate.
Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of the quantum computational networks with these gates may be achieved with the help of the operator algebra structure of Hamiltonians of the systems and the properties of the multiple-quantum operator algebra subspaces of the Liouville operator space and the specific properties of the quantum algorithm corresponding to the quantum network. As an example, the two-qubit diagonal gates are exactly prepared in detail in superconducting Josephson junctions.
The two-level systems (TLSs) naturally occurring in Josephson junctions constitute a major obstacle for the operation of superconducting phase qubits. Since these TLSs can possess remarkably long decoherence times, we show that such TLSs can themselves be used as qubits, allowing for a well controlled initialization, universal sets of quantum gates, and readout. Thus, a single current-biased Josephson junction can be considered as a multiqubit register. It can be coupled to other junctions to allow the application of quantum gates to an arbitrary pair of qubits in the system. Our results indicate an alternative way to realize superconducting quantum information processing.
The superconducting phase qubit combines Josephson junctions into superconducting loops and defines one of the promising solid state device implementations for quantum computing. While conventional designs are based on magnetically frustrated superconducting loops, here we discuss the advantages offered by πππ-junctions in obtaining naturally degenerate two-level systems. Starting from a basic five-junction loop, we show how to construct degenerate two-level junctions and superconducting phase switches. These elements are then effectively engineered into a superconducting phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting phase qubits can be understood as the macroscopic analogue of the `quiet' s-wave-d-wave-s-wave Josephson junction qubits introduced by Ioffe {\it et al.} [Nature {\bf 398}, 679 (1999)].
Two-level system fluctuators in superconducting devices have demonstrated coherent coupling with superconducting qubits. Here, we show that universal quantum logic gates can be realized in these two-level systems solely by tuning a superconducting resonator in which they are imbedded. Because of the large energy separation between the fluctuators, conventional gate schemes in the cavity QED approach that are widely used for solid-state qubits cannot be directly applied to the fluctuators. We study a scheme to perform the gate operations by exploiting the controllability of the superconducting resonator with realistic parameters. Numerical simulation that takes into account the decay of the resonator mode shows that the quantum logic gates can be realized with high fidelity at moderate resonator decay rate. The quantum logic gates can also be realized between fluctuators inside different Josephson junctions that are connected by a superconducting loop. Our scheme can be applied to explore the coupling between two-level system fluctuators and superconducting resonators as well as the coherent properties of the fluctuators.