A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an arti®cial twolevel electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed 1±4 . The Cooper-pair box has therefore been suggested 5±7 as a candidate for a quantum bit or qubit'Ðthe basic component of a quantum computer. Here we report the observation of quantum oscillations in a singleCooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modi®es the energies of the two charge states nonadiabatically, bringing them into resonance. The resulting stateÐ a superposition of the two charge statesÐis detected by a tunnelling current through a probe junction. Our results demonstrate electrical coherent control of a qubit in a solid-state electronic device.Rapidly improving nanofabrication technologies have made quantum two-level systems in solid-state devices promising for functional quantum circuit integration. To coherently control an individual two-level system as a unit of such circuits, several systems have been examined, such as electronic 8±10 and spin 11 states in quantum dots, nuclear spins of impurity atoms embedded in a substrate 12 , and magnetic-¯ux states in a superconducting ring 13,14 . However, only optical coherent control has been realized experimentally 10 .A single-Cooper-pair box 1 (Fig. 1) is a unique arti®cial solid-state system in the sense that: (1) although there are a large number of electrons in the metal`box' electrode, under superconductivity they all form Cooper pairs and condense into a single macroscopic ground state, |ni, separated by a superconductivity gap ¢ from the excited states with quasiparticles. (Here |ni denotes the chargenumber state with the excess number of electrons n the box, n.) (2) The only low-energy excitations are the transitions between different |ni states due to Cooper-pair tunnelling through the Josephson junction, if ¢ is larger than the single-electron charging energy of the box E C . (3) E C , if larger than the Josephson energy E J and the thermal energy k B T, suppresses a large¯uctuation of n. Hence, we can consider the system an effective two-level system by taking into account the two lowest-energy states which differ by one Cooper pair. (4) In addition, the relative energy of the two levels can be controlled through the gate voltage. For example, as shown in Fig. 2a, the electrostatic energies, E C n 2 Q t =e 2 , of two such charge states |0i and |2i change as a function of the total gate-induced charge Q t and cross each other at Q t =e 1. (The parabolic background energy is subtracted.) In the presence of Josephson coupling, and with weak enough dissipation 15 , these charge states w...

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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.

We have developed a Josephson parametric amplifier, comprising a superconducting coplanar waveguide resonator terminated by a dc SQUID (superconducting quantum interference device). An external field (the pump, ∼ 20 GHz) modulates the flux threading the dc SQUID, and, thereby, the resonant frequency of the cavity field (the signal, ∼ 10 GHz), which leads to parametric signal amplification. We operated the amplifier at different band centers, and observed amplification (17 dB at maximum) and deamplification depending on the relative phase between the pump and the signal. The noise temperature is estimated to be less than 0.87 K.Degenerate parametric amplifiers are phase sensitive amplifiers, which can in principle amplify one of the two quadratures of a signal without introducing extra noise. 1,2 Parametric amplifiers based on the nonlinear inductance of a Josephson junction have been studied for a long time, 3 including one which demonstrated vacuum noise squeezing. 4 Recently, there has been a renewed interest in parametric amplifiers 5,6,7 due in part to the increasing need for quantum-limited amplification in the field of quantum information processing using superconducting circuits. 8,9 In the present work, we design a Josephson parametric amplifier, comprising a superconducting transmissionline resonator terminated by a dc SQUID (superconducting quantum interference device). Contrary to the previous works, the pump is not used to directly modulate a current through the Josephson junction, but is instead used to modulate a flux through the dc SQUID. 10 The resonant frequency of the resonator, namely, the band center of the signal, is widely controllable by a dc flux also applied to the SQUID (see also Ref. [7]). Moreover, as the pump and the signal are applied to different ports and their frequencies are twice different (see below), it is straightforward to separate the output signal from the pump. This is a unique property of the fluxpumping scheme; it arises because the finite dc flux bias allows linear coupling of the pump even in the absence of a dc current bias across the SQUID. 11 We operated such a flux-driven parametric amplifier and characterized its basic properties. Figure 1a shows a schematic diagram of the flux-driven parametric amplifier. The primary component of the amplifier is a transmission-line resonator defined by its coupling capacitance C c and a dc SQUID termination. The magnetic flux Φ penetrating the SQUID loop changes the boundary condition of the resonator at the right end (by the change of the Josephson inductance), and hence enables us to control the resonant frequency. 12,13 The resonant frequency f 0 for the first mode (λ/4 ≥ d, where λ is the wavelength and d is the cavity length) is schematically drawn as a function of Φ/Φ 0 in Fig. 1b, where Φ 0 is a flux quantum (see also Fig. 2a). We now assume the cavity resonance is set to a particular value, f 0dc , by applying a dc flux Φ dc (open circle in the figure). We then apply microwaves at a frequency 2f 0dc to the pump line wh...

To do large-scale quantum information processing, it is necessary to control the interactions between individual qubits while retaining quantum coherence. To this end, superconducting circuits allow for a high degree of flexibility. We report on the time-domain tunable coupling of optimally biased superconducting flux qubits. By modulating the nonlinear inductance of an additional coupling element, we parametrically induced a two-qubit transition that was otherwise forbidden. We observed an on/off coupling ratio of 19 and were able to demonstrate a simple quantum protocol.

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A hundred years after discovery of superconductivity, one fundamental prediction of the theory, the coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect: whilst the latter is a coherent transfer of charges between superconducting contacts 2,3 , the former is a

We investigated temporal behavior of an artificial two-level system driven by a strong oscillating field; namely, quantum-state evolution between two charge states in a small Josephson-junction circuit irradiated with microwaves. Rabi oscillations corresponding to 0-, 1-, and 2-photon resonances were observed. As a function of microwave amplitude, the Rabi frequencies followed a first-kind Bessel function of the corresponding order to the number of photons.