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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Coupled Josephson quantum bits

Jaw-Shen Tsai, Tsuyoshi Yamamoto, Yu. A. Pashkin, O. V. Astafiev, Yasunobu Nakamura

Published May 25, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.547408

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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.
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.
A practical quantum computer, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions have been implemented; these exploit the coherence of Cooper-pair tunnelling in the superconducting state. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates--a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.
We have succeeded in coupling two solid-state qubits and observing quantum coherent dynamics of such a system. Each qubit is a Cooper-pair box whose quantum states are manipulated by means of pulse technique. Coupling of the two qubits is done by using a small on-chip capacitor. For read-out of the state of each qubit, we use probe electrodes connected to the Cooper-pair boxes through resistive tunnel junctions. Quantum coherent oscillation of the two-qubit charge states results in the oscillation of the probe currents. The observed "beatings" as well as avoided level crossing in the energy spectrum is a direct evidence for the interaction of the two qubits. Although we could not measure the amount of entanglement directly, our simulations based on the experimental data show that during quantum evolution the qubits remain entangled most of the time. A straightforward continuation of this experiment is a demonstration of conditional gate operation, a prototype of a solid-state quantum logic gate.
The concept of a quantum computer was invented in the beginning of the 1980s as a quantum generalization of the reversible classical computer. After discoveries in the middle of the 1990s of quantum algorithms, which wouldsolve some problems considered intractable for classical computers, the field of quantum computing has developed rapidly. A wide range of quantum systems are investigated for their possible ability to implement quantum algorithms in practice. The most promising solid state implementations are superconducting electrical circuits based on the Josephson effect, and the Coulomb blockade effect. Superconducting circuits are macroscopic quantum systems which can be fabricated using standard lithography technologies. Superconducting qubits - basic building blocks of a quantum computer - have been developed at several research laboratories, among others the MC2 here at Chalmers. This thesis presents a theoretical investigation of controllable coupling of superconducting qubits based on the single Cooper-pair box. Two coupling schemes are investigated in detail: current-controlled coupling via large Josephson junctions, and coupling via a superconducting stripline cavity. Both coupling designs are scalable and suitable for the charge regime of the single Cooper-pair box, as well as for the charge-phase regime where the qubit is better protected from environmental noise. Quantum gate protocols which are relevant for these physical couplings are discussed. The investigations show that, for both considered designs, the simplest two-qubit gate is the conditional phase-shift gate. This gate is universal for quantum computing, and it can create maximallyentangled qubit pairs in only one run. The investigation combines methods from electrical engineering, quantum mechanics and quantum computer science.
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.