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arXiv:cond-mat/0603753 · Physical Review Letters

Quantum Two-Level Systems in Josephson Junctions as Naturally Formed Qubits

Alexandre M. Zagoskin, Sahel Ashhab, J. R. Johansson, Franco Nori

Published Aug 14, 2006• 118 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.97.077001

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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.
We study the decoherence dynamics of a superconducting qubit coupled to a quantum two-level system (TLS) in addition to its weak coupling to a background environment [1]. We identify two weak-coupling regimes, which differ by the relation between qubit and TLS decoherence times, and a strong coupling regime. We find expressions for the qubit decoherence rates in the weak-coupling regimes. For a weakly coupled and strongly dissipative TLS we find that the qubit dynamics is markovian, whereas for a weakly dissipative TLS the qubit dynamics shows non-markovian behavior. In the strong-coupling regime we study the driven qubit dynamics and we analyze the differences from standard Rabi-oscillations due to the coupling to the quantum TLS [2]. In doing so we identify signatures in the qubit dynamics that can be used to characterize the TLS. We also investigate the possibility of using environmental TLSs with long coherence times for quantum information processing [3]. By using the Josephson junction as a bus and the TLSs in the environment as qubits, we demonstrate that initialization, a universal set of quantum gates, and read-out of the TLSs can be implemented, even though the TLSs themselves cannot be directly accessed.
Two-level system fluctuators (TLS's) in the tunnel barrier of a Josephson junction have recently been demonstrated to cause novel energy splittings in spectroscopic measurements of superconducting phase qubits. With their strong coupling to the Josephson junction and relatively long decoherence times, TLS's can be considered as potential qubits and demonstrate coherent quantum effects. Here, we study the effective interaction between the TLS qubits that is mediated by a Josephson junction resonator driven by an external microwave source. This effective interaction can enable controlled quantum logic gates between the TLS's. Our study can be extended to other superconducting resonators coupling with TLS's.
Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.
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.