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arXiv:cond-mat/0306207 · Physical review. B, Condensed matter

Quantum information processing with superconducting qubits in a microwave field

J. Q. You, Franco Nori

Published Aug 22, 2003• 375 citations
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Abstract

We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multiphoton processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.

DOI
10.1103/physrevb.68.064509

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We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multiphoton processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
We study theoretically dynamic properties of an interferometer-type Josephson charge qubit consisting of a single-Cooper-pair transistor (with capacitive gate) closed by a superconducting inductive loop. Analyzing the radio frequency response of the device to microwave fields within a two-band model, we present basic features of a method for observation of various Rabi oscillation modes. For this purpose, we apply the dressed-state approach in conjunction with the rotating-wave approximation to the strongly driven quantum bit. We demonstrate the existence of multiphoton excitations and Rabi frequency transitions between quantum levels connected with them. The resulting oscillations of the supercurrent in the interferometer modify the spectral loop susceptibility. This effect may be detected via the coil of a high-quality tank circuit inductively coupled to the qubit by measuring the tank-qubit impedance variations belonging to it.
We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.
Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.
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 latest breakthroughs in microwave quantum photonics in superconducting circuits are presented. Advancing technologies of Josephson junction quantum bits (qubits) have been applied to control and measurement of itinerant microwave fields. Methods to generate nonclassical microwave states such as single-photon states and squeezed states have been developed. Techniques to characterize those nonclassical itinerant states have also been established. They are ready to be combined to demonstrate various quantum protocols, which extend the possibilities of quantum information processing, quantum metrology, and quantum communications using superconducting circuits.