We propose a scheme to implement variable coupling between two flux qubits using the screening current response of a dc Superconducting QUantum Interference Device (SQUID). The coupling strength is adjusted by the current bias applied to the SQUID and can be varied continuously from positive to negative values, allowing cancellation of the direct mutual inductance between the qubits. We show that this variable coupling scheme permits efficient realization of universal quantum logic. The same SQUID can be used to determine the flux states of the qubits.Comment: 4 pages, 4 figure
We report measurements on two superconducting flux qubits coupled to a readout Superconducting QUantum Interference Device (SQUID). Two on-chip flux bias lines allow independent flux control of any two of the three elements, as illustrated by a two-dimensional qubit flux map. The application of microwaves yields a frequency-flux dispersion curve for 1-and 2-photon driving of the single-qubit excited state, and coherent manipulation of the single-qubit state results in Rabi oscillations and Ramsey fringes. This architecture should be scalable to many qubits and SQUIDs on a single chip.PACS numbers: 03.67. Lx, 85.25.Cp, 85.25.Dq Superconducting quantum bits (qubits) based on charge [1,2], magnetic flux [3,4], and phase difference across a Josephson junction [5,6] are attractive candidates for the basis of a quantum computer because of their inherent scalability using established thin-film fabrication techniques. Advantages of the flux qubit include its immunity to the ubiquitous charge noise in the substrate and that it can be configured with no direct electrical connections. One type of flux qubit consists of a superconducting loop interrupted by three Josephson junctions with critical currents I 0 , I 0 , and αI 0 (α < 1) [7]. When the applied flux bias Φ Q is at a degeneracy point (n+1/2)Φ 0 (n is an integer such that |Φ Q −nΦ 0 | ≤ Φ 0 /2; Φ 0 ≡ h/2e is the flux quantum), a screening supercurrent J Q can flow in either direction around the loop. The ground and first excited states of the qubit correspond to symmetric and antisymmetric superpositions of the two current states and are separated by an energy ∆. Here, ∆/h is the tunnel frequency between the current states, typically a few GHz. When Φ Q is away from a degeneracy point, the energy difference between the two superposed states is ν = (The state of the qubit is measured by coupling the screening flux generated by J Q to a hysteretic dc superconducting quantum interference device (SQUID). This flux determines the bias current at which the SQUID switches out of the zero-voltage state.In addition to the development of scalable interqubit couplings [8], a prerequisite for scaling to a system of many qubits is that the attendant readout, filtering, and bias circuitry also scale. A particular challenge is that the flux bias must be settable for each element individually. This mandates the use of on-chip flux-bias lines in an arrangement that enables one to apply a combination of currents to address any given qubit or SQUID while maintaining all other flux biases at constant values. Furthermore, the bias currents required to change the flux over (say) ±1Φ 0 should not be so large that it becomes impractical to deliver them to a chip cooled to millikelvin temperatures. This requirement establishes minimum self-inductances of the qubit and readout SQUID that are substantially larger than values used previously in 3-junction qubits, which have relied on external coils to generate large magnetic fields [4,9,10]. At the same time, the mutual inductance between ...
We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro-and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.
The Central European Watershed divides the Rhine-Main catchment and the Danube catchment. In the Early Medieval period, when ships were important means of transportation, Charlemagne decided to link both catchments by the construction of a canal connecting the Schwabian Rezat and the Altmühl rivers. The artificial waterway would provide a continuous inland navigation route from the North Sea to the Black Sea. The shortcut is known as Fossa Carolina and represents one of the most important Early Medieval engineering achievements in Europe. Despite the important geostrategic relevance of the construction it is not clarified whether the canal was actually used as a navigation waterway. We present new geophysical data and in situ findings from the trench fills that prove for the first time a total length of the constructed Carolingian canal of at least 2300 metres. We have evidence for a conceptual width of the artificial water course between 5 and 6 metres and a water depth of at least 60 to 80 cm. This allows a crossing way passage of Carolingian cargo scows with a payload of several tons. There is strong evidence for clayey to silty layers in the trench fills which reveal suspension load limited stillwater deposition and, therefore, the evidence of former Carolingian and post-Carolingian ponds. These findings are strongly supported by numerous sapropel layers within the trench fills. Our results presented in this study indicate an extraordinarily advanced construction level of the known course of the canal. Here, the excavated levels of Carolingian trench bottoms were generally sufficient for the efficient construction of stepped ponds and prove a final concept for a summit canal. We have evidence for the artificial Carolingian dislocation of the watershed and assume a sophisticated Early Medieval hydrological engineering concept for supplying the summit of the canal with adequate water.
We have demonstrated strong antiferromagnetic coupling between two three-junction flux qubits based on a shared Josephson junction, and therefore not limited by the small inductances of the qubit loops. The coupling sign and magnitude were measured by coupling the system to a high-quality superconducting tank circuit. Design modifications allowing to continuously tune the coupling strength and/or make the coupling ferromagnetic are discussed. DOI: 10.1103/PhysRevB.72.020503 PACS number͑s͒: 74.50.ϩr, 85.25.Am, 85.25.Cp Quantum superposition of macroscopic states was conclusively demonstrated in superconducting Josephson structures in 2000 ͑Ref. 1͒. Such structures are natural candidates for the role of qubits ͑quantum bits͒, the constituent elements of quantum computers. Successful operation of a quantum computer would be the ultimate confirmation of the validity of quantum mechanics on the macroscopic scale, which makes the task of controllably linking a significant number of qubits more than just an advance in technology.The coupling energy J must be comparable to the splittings between the two lowest eigenstates of individual qubits. On the other hand, the coupling must not excite the qubits to higher levels, or significantly increase the qubits' interaction with undesirable degrees of freedom, leading to decoherence and dissipation. Finally, J should be either variable by design or, even better, tunable during the system's operation.We demonstrate the coupling of two three-Josephsonjunction ͑3JJ͒ flux qubits, making progress towards meeting these requirements, and discuss the ways of its further improvement. The 3JJ qubit consists of a superconducting loop with small inductance L interrupted by three Josephson junctions. The two different directions of persistent current in the loop form the qubit's basis states.2 The 3JJ design enables classical bistability even for L → 0, resulting in a weak coupling to environmental magnetic-flux noises. As a result, quantum behavior with long decoherence times was observed in this type of qubit by several groups. [3][4][5] However, their small L makes it difficult to couple 3JJ qubits inductively; generally, J is smaller than the singlequbit level splitting. We therefore implement the proposals 6,7 to directly link two qubits through a shared junction ͑Fig. 1͒. The resulting coupling not only is strong, but can also be varied independently of other design parameters by choosing the shared junction's size.To calculate J, we neglect the inductances so that the potential term in the Hamiltonian contains only the Josephson energy U J =−͚ j=0 6 E j cos j , and use flux quantization ͑2͒where2 is the persistent current in a free 3JJ qubit.2 Inserting these into U J , one finds that the AF states have the lower energy byso that the effective mutual inductance ប 2 /4e 2 E 0 is just the standard Josephson inductance of the coupling junction. PHYSICAL REVIEW B 72, 020503͑R͒ ͑2005͒
We studied and optimised the properties of ultrathin superconducting niobium nitride films fabricated with a plasma-enhanced atomic layer deposition (PEALD) process. By adjusting process parameters, the chemical embedding of undesired oxygen into the films was minimised and a film structure consisting of mainly polycrystalline niobium nitride with a small fraction of amorphous niobium oxide and niobium oxo-nitrides were formed. For this composition a critical temperature of 13.8 K and critical current densities of 7 × 106 A cm–2 at 4.2 K were measured on 40 nm thick films. A fundamental correlation between these superconducting properties and the crystal lattice size of the cubic δ-niobium-nitride grains were found. Moreover, the film thickness variation between 40 and 2 nm exhibits a pronounced change of the electrical conductivity at room temperature and reveals a superconductor–insulator-transition in the vicinity of 3 nm film thickness at low temperatures. The thicker films with resistances up to 5 kΩ per square in the normal state turn to the superconducting one at low temperatures. The perfect thickness control and film homogeneity of the PEALD growth make such films extremely promising candidates for developing novel devices on the coherent quantum phase slip effect.
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