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CRC Press eBooks

Coherent Dynamics and Quantum Information Processing in Josephson Charge Devices

Ping Sheng, Zikang Tang

Published Mar 6, 2003• 0 citations
Publisher

Abstract

Quantum information technology focuses on the quantum-state engineering of a \nsystem, with which the quantum states of the system can be prepared, manipulated \nand readout quantum mechanically. Recently, the "macroscopic" quantum effects \nin low-capacitance Josephson-junction circuits have received renewed attention \nbecause suitable Josephson devices may be used as qubits for quantum \ninformation processing (QIP) (Makhlin et al., 1999, 2001 and Mooij et al., \n1999) and are expected to be scalable to large-scale circuits using modern micro \nfabrication techniques.

DOI
10.1201/9780203390283-37

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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

•Jan 1, 1999•16 citations
Quantum information technology focuses on the quantum-state engineering of a \nsystem, with which the quantum states of the system can be prepared, manipulated \nand readout quantum mechanically. Recently, the "macroscopic" quantum effects \nin low-capacitance Josephson-junction circuits have received renewed attention \nbecause suitable Josephson devices may be used as qubits for quantum \ninformation processing (QIP) (Makhlin et al., 1999, 2001 and Mooij et al., \n1999) and are expected to be scalable to large-scale circuits using modern micro \nfabrication techniques.
Quantum-state engineering, i.e., active control over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. With concepts developed in atomic and molecular physics and in the context of NMR, the field has been stimulated further by the perspectives of quantum computation and communication. Low-capacitance Josephson tunneling junctions offer a promising way to realize quantum bits (qubits) for quantum information processing. The article reviews the properties of these devices and the practical and fundamental obstacles to their use. Two kinds of device have been proposed, based on either charge or phase (flux) degrees of freedom. Single- and two-qubit quantum manipulations can be controlled by gate voltages in one case and by magnetic fields in the other case. Both kinds of device can be fabricated with present technology. In flux qubit devices, an important milestone, the observation of superpositions of different flux states in the system eigenstates, has been achieved. The Josephson charge qubit has even demonstrated coherent superpositions of states readable in the time domain. There are two major problems that must be solved before these devices can be used for quantum information processing. One must have a long phase coherence time, which requires that external sources of dephasing be minimized. The review discusses relevant parameters and provides estimates of the decoherence time. Another problem is in the readout of the final state of the system. This issue is illustrated with a possible realization by a single-electron transistor capacitively coupled to the Josephson device, but general properties of measuring devices are also discussed. Finally, the review describes how the basic physical manipulations on an ideal device can be combined to perform useful operations.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ 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. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
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.
Superconducting (SC) circuits can behave like atoms making transitions between a few energy levels. Such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip. This talk overviews a few of our theoretical studies on SC circuits and quantum information processing (QIP) including: SC qubits for single photon generation and for lasing; controllable couplings among qubits; how to increase the coherence time of qubits using a capacitor in parallel to one of the qubit junctions; hybrid circuits involving both charge and flux qubits; testing Bell’s inequality in SC circuits; generation of GHZ states; quantum tomography in SC circuits; preparation of macroscopic quantum superposition states of a cavity field via coupling to a SC qubit; generation of nonclassical photon states using a SC qubit in a microcavity; scalable quantum computing with SC qubits; and information processing with SC qubits in a microwave field. Controllable couplings between qubits can be achieved either directly or indirectly. This can be done with and without coupler circuits, and with and without data-buses like EM fields in cavities (e.g., we will describe both the variable-frequency magnetic flux approach and also a generalized double-resonance approach that we introduced). It is also possible to “turn a quantum bug into a feature” by using microscopic defects as qubits, and the macroscopic junction as a controller of it. We have also studied ways to implement radically different approaches to QIP by using “cluster states” in SC circuits.
Recent demonstrations of macroscopic quantum coherence in Josephson junction based electronic circuits have opened an entirely new dimension for research and applications in the established field of Josephson electronics. In this article we discuss basic Josephson circuits for qubit applications, methods of quantum description of these circuits, and circuit solutions for qubit couplings. Principles of manipulation and readout of superconducting qubits are reviewed and illustrated with recent experiments using various qubit types.
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