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arXiv:cond-mat/9912405 · Journal of Low Temperature Physics

Nano-Electronic Realizations of Quantum Bits

Yuriy Makhlin, Gerd Schön, Alexander Shnirman

Published Mar 1, 2000• 13 citations
arXivHTMLPDF
DOI
10.1023/a:1004655831368

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Nano-Electronic Realizations Of Quantum Bits

Yuriy Makhlin, Gerd Schön, Alexander Shnirman

INTRODUCTION Quantum computers, if available, could perform certain operations in a massive parallel way, which would lead to an exponential speed-up as compared to the performance of classical computers. Furthermore, mediumsize quantum information processing devices could be used in a number of applications such as, for instance, quantum communication and quantum cryptography. Several physical realizations of quantum bits, i.e. the elementary building blocks of quantum computers, have been proposed. The best studied ones are trapped ions, NMR in the liquid state and cavity QED. Here we discuss solid-state nano-electronic realizations. They appear promising since they can be scaled up to large numbers of qubits and are most easily Yu. Makhlin, G. Schon, and A. Shnirman embedded in electronic circuits. Josephson junction circuits are particularly suitable for quantum information processing, since they combine the intrinsic coherence of the superconducting state

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Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.

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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.

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INTRODUCTION Quantum computers, if available, could perform certain operations in a massive parallel way, which would lead to an exponential speed-up as compared to the performance of classical computers. Furthermore, mediumsize quantum information processing devices could be used in a number of applications such as, for instance, quantum communication and quantum cryptography. Several physical realizations of quantum bits, i.e. the elementary building blocks of quantum computers, have been proposed. The best studied ones are trapped ions, NMR in the liquid state and cavity QED. Here we discuss solid-state nano-electronic realizations. They appear promising since they can be scaled up to large numbers of qubits and are most easily Yu. Makhlin, G. Schon, and A. Shnirman embedded in electronic circuits. Josephson junction circuits are particularly suitable for quantum information processing, since they combine the intrinsic coherence of the superconducting state
Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.
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.