Superconducting Qubits : Quantum Computing with Josephson Junctions

Although coherent super-positions of quantum states have already been demonstrated in qubit circuits, the manipulation methods used were still rather primitive and mainly limited to Rabi precession. The aim of the result #21684 "NMR-style operation of the Quantronium qubit" is to precisely demonstrate that sophisticated NMR methods can be applied for manipulating the quantum state of a qubit and obtain detailed information on decoherence processes. Proving that arbitrary and robust transformations of the qubit state can be performed is indeed an essential issue. The present result proves that NMR methods can be successfully used in order to achieve this goal, even if the accuracy and fidelity of presently achieved operation are still insufficient. The main results are described in the first document: - "NMR-like Control of a Quantum Bit Super-conducting Circuit" (to appear in Phys. Rev. Lett.). The other documents describe some parts of the result more in detail. We have demonstrated in particular that: 1) rotations of the effective spin representing the qubit can be combined and do yield to the predicted results. This was achieved by measuring the qubit state after a two-pulse sequence with different rotation axes, as a function of the time delay between pulses. This Ramsey interference experiment allows probing the combined rotation performed by the two rotations. We have found good agreement with theoretical predictions. 2) arbitrary transformations of the qubit state can thus be achieved by combining three pulses with orthogonal rotation axes, which is achieved by using microwave pulses with phases differing by pi/2. Although this result was expected, its proof was essential. 3) robust rotations can be performed by using the composite pulse methods developed in NMR. We have demonstrated improved robustness respectively to frequency detuning using a Corpse pulse sequence. Quantum Computing requires an accuracy that has been marginally reached in NMR, despite 50 years of continuous development. Composite pulses provide the most accurate method to implement robust rotations in NMR. Demonstrating that these methods also apply to qubits paves the way to more sophisticated qubit operations. 4) Various other NMR methods can be used. We have in particular exploited the NMR spin-locking technique in order to measure relaxation and decoherence of the qubit in presence of a driving microwave field. We have found that relaxation in the driven situation is slower than during free evolution in the lab frame. This result rises the question of actively fighting decoherence. Since the Quantum Error Correcting Codes are to difficult to implement in circuits presently, we look for "analog" methods able tio fight decoherence. We found that driving the qubit can indeed increase the effective relaxation and coherence times. Note that a similar result has been recently obtained for the flux qubit. 5) the spin-echo technique, used to suppress inhomogeneous broadening in NMR, can be used to suppress the effect of low frequency temporal fluctuations of the qubit parameters. We have demonstrated that a significant increase of the coherence time can be obtained with this method. We have found in particular that the charge noise spectrum decreases faster than the expected 1/f law at high frequency, above 1MHz. This unexpected result raises the interest of the Cooper pair box, which suffers from charge noise. Our partners already benefit from the result, which is presently the state of the art for qubit manipulation in super-conducting circuits. Other teams involved in qubit circuits will also certainly use the methods that we have applied to the quantronium. The published documents provide the necessary information for using the result, which has been communicated in international conferences, and in three international Quantum Computing schools during year 2004.

This work describes a new solution for controllable physical qubit-qubit coupling of charge and charge-phase qubits based on Josephson junctions (JJ). The network has the following properties: (a) nearest-neighbour qubit-qubit coupling controlled by external bias current, (b) qubits parked at the degeneracy points, also during qubit-qubit interaction, (c) separate knobs for controlling individual qubits and qubit-qubit coupling, (d) scalability. An important feature is that the network is easily fabricated, and is in line with current mainstream experiments. There are many proposed schemes for two (multi)-qubit gates where an effective qubit coupling is controlled by tunings of qubits or bus resonators. However, there are also suggestions how to control physical qubit interaction, most of which require local magnetic field control. Recently, Yamamoto et al. successfully implemented a CNOT gate using fixed capacitive coupling between two charge qubits, controlling the effective qubit-qubit interaction by tuning single-qubit level splittings into resonance - however, this method might not be well suited for more advanced gates on charge qubits because of strong decoherence when qubits are operated away from the degeneracy points. We therefore design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighbouring qubit loops via local dc-current gates. The network under consideration consists of a chain of charge qubits - Single Cooper Pair Transistors (SCT) - with loop-shaped electrodes coupled together by current biased coupling JJs at the loop intersections. The loop design creates an (inductive) interface to the qubit by means of circulating currents, which has been used as a tool for qubit readout by Vion et al. We employ these current states in the qubit loops to create controllable coupling of neighbouring qubits. The results are derived in the charge qubit limit EC >> EJ. However, the analysis and the coupling mechanism also apply to the case of EC approximately equal to EJ, describing the charge-phase qubit. Left without any external current biasing of the coupling and readout JJs, the network acts as a quantum memory of independent qubits (neglecting a weak residual interaction). When a bias current is sent through the coupling JJ, the current-current interaction between the neighbouring qubits is switched on and increases with increasing bias current. This provides a realistic solution for easy local control of the physical coupling of charge qubits via current biasing of coupling JJs or, alternatively, pairs of readout junctions. The design is in line with experimental mainstream development of charge qubit circuits and can easily be fabricated and tested experimentally. Most importantly, it allows readout via currently tested methods that promise single-shot projective measurement and even non-destructive measurements, via e.g. RF-reflection readout of a JJ threshold detector or an SET. The tuneable coupling of the qubit chain allows easy implementation of CNOT and CNOT-SWAP operations. Independent two-qubit operations can be performed in parallel when the network consists of five qubits or more, and generalization to single-shot N-qubit gates seems possible. This may offer interesting new opportunities for operating qubit clusters in parallel and swapping and teleporting qubits along the chain, for experimental implementations of elementary quantum information processing.

We have developed a method to rapidly measure the switching current of a Josephson tunnel junction with low critical current. Measuring at low critical current presents a problem for fast measurement because the rise time of the voltage at the top of the cryostat is ultimately set by the time needed to charge the lead capacitance with a very small current. Cold amplifiers mounted close to the junction can be used to reduce the input capacitance, but this technique presents other problems and is not simple to implement.

We have implemented a non-destructive method for the readout of a persistent current flux qubit. The detection is based on the measurement of the Josephson inductance of a DC super-conducting quantum interference device (DC-SQUID) inductively coupled to the qubit. The SQUID is included in a resonant circuit, allowing for high flux sensitivity. The measurement strength can be tuned with the amplitude of the RF-signal used to drive the resonant circuit. The method eliminates the disadvantages of the strongly dissipative state associated with the switching of a Josephson junction to the voltage state. Using this method, we have measured the spectroscopy and the relaxation time of a flux qubit, obtaining relaxation times of the order of 80 microseconds. The measurement has high efficiency and further improvement is possible, by optimising the measurement circuit. This detector can be used for experimental studies of the relation between quantum measurement and decoherence, as well as for correlation measurements on two qubits.

The interest in quantum computation, in particular, is stimulated by the discovery of quantum algorithms, which can outperform their classical counterparts in solving problems of significant practical relevance. In the field of solid-state quantum computation, and in particular in the area of super-conducting nano-circuits, considerable progress has been made in the field of quantum hardware. It is equally important in the development of quantum computing to experimentally realize complete quantum algorithms. It is also particularly important to see whether at the present it is already possible to implement also quantum algorithms using super-conducting nanocircuits. We showed how the Deutsch algorithm and the Bernstein-Vazirani algorithm can be run on a Josephson quantum computer. We analyse the experiment by Nakamura et al in terms of quantum interferometry and show that it corresponds to the implementation of the one-qubit version of Deutsch's algorithm. By generalizing this idea we show how the N-qubit Deutsch algorithm, with N<3, can be implemented. Finally we showed explicitly that the Bernstein-Vazirani algorithm can be implemented using uncoupled qubits (for arbitrary N). Therefore it can be realized by means of the set-up of Nakamura et al. experiment. Our proposed implementation realizes the algorithms by using only state-of-the-art technology. A peculiarity is that the gate operations representing the algorithm are carried out in a basis, which is different from the one, which is measured. This helped us to obtain the desired results with a minimum number of operations. Thus, one may hope to see the expected behaviour of the system even with the decoherence times which are measured at the present in these systems. In addition the experimental implementation of this proposal may serve to study entanglement and decoherence on entangled states in great details. The methods outlined above can also be used to study other interesting problems such as the production and measurement of Bell states and GHZ states. From a practical point of view, it would be particularly interesting to find ways to create such states in a 'single shot' with one appropriate gate operation. Even though it appears rather difficult to avoid the locality loophole in this kind of set-up it is nevertheless a remarkable challenge to measure such quantum correlations in a macroscopic system.

We have used a Single Electron Transistor operated in the Radio Frequency mode (RF-SET) to read out the quantum information of a single Cooper-pair Box, which acts as a qubit. We have analysed the frequency dependent back action from the RF-SET on the qubits and are able to calculate relaxation and decoherence times from our model. The back action is due both to shot noise and to quantum fluctuations of the SET. The conclusion is that relaxation can be minimized by increasing the qubit energy splitting. Another conclusion is that the dephasing can be drastically reduced by turning of the bias of the SET and by turning on the Coulomb blockade in the SET, by changing the gate voltage of the SET.

We have studied the switching behaviour of a small capacitance Josephson junction both in experiment, and by numerical simulation of a model circuit. The switching is a complex process involving the transition between two dynamical states of the non-linear circuit, arising from a frequency dependent damping of the Josephson junction. We show how a specific type of bias pulse-and-hold, can result in a fast detection of switching, even when the measurement bandwidth of the junction voltage is severely limited, and/or the level of the switching current is rather low.

Recent experiments with Josephson-junction circuits demonstrated long-lived coherent oscillations. They had acquired a resolution sufficient for detailed studies of the dephasing times and decay laws, stressing the need for the theory analysis of the dissipative dynamics of qubits subject to relevant noise sources. In solid-state systems decoherence is potentially strong due the host of microscopic modes. In Josephson qubits the noise is dominated by material-dependent sources, such as background-charge fluctuations or variations of critical currents and magnetic fields, with power spectrum peaked at low frequencies, often proportional to 1/f. A further relevant contribution is the electromagnetic noise of the control circuit, typically Ohmic at low frequencies. The 1/f noise appears difficult to suppress and, since the dephasing is dominated by low-frequency noise, it is particularly destructive. On the other hand, Vion et al showed that the effect of this noise can be substantially reduced by tuning the linear longitudinal qubit-noise coupling to zero. The same strategy, suppressing the linear qubit-detector coupling, was used to minimize the effect of the quantum detector in the off-state. The coherence time achieved in this way was 2 orders of magnitude longer than in earlier experiments. Motivated by these experiments with Josephson-junction circuits, we analyse the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We studied the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. An Ohmic noise coupling linearly to the qubit lead sto a decoherence rate which scales proportional to the temperature T, for quadratic coupling this low changes into a T3 dependence. For 1/f noise and Gaussian noise the decay is proportional to exp (-const t2). Our analysis shows, however, that non-Gaussian effects are strong and lead to a power law decay. For further details we refer to our publication: Dephasing at optimal points, Y. Makhlin and A. Shnirman, Phys. Rev. Lett. 92, 178301 (2004). For quantum information technology it is necessary to investigate properties of real physical systems used as quantum detectors. Certain quantum algorithms require an efficient (single-shot) read out the final state of a qubit. This can be done by either strongly coupled threshold detectors, or by "measurement in stages" strategy. For weakly coupled detectors the only way to perform single-shot measurements is to be in the quantum-non-demolition (QND) regime, i.e., by measuring an observable, which commutes with the Hamiltonian and is, thus, conserved. In our work we concentrated on continuous weak non-QND measurements (monitoring) of the coherent oscillations of a qubit (two-level system, spin-1/2). This regime is realized, e.g., for the transverse coupling between the spin and the meter, e.g., when the effective magnetic field acting on the spin is along the x-axis while the component along the z-axis is being measured. In this case one observes the stationary state properties of the system, after the information about the initial state of the qubit is lost. Thus, this regime is not useful for quantum computation. Yet, studying the properties of the meter in the stationary monitoring regime, one can obtain information necessary in order to employ the meter in the QND regime. Another motivation for our study comes from the recent activity in the STM single spin detection. For further details we refer to our publication: Output spectrum of a measuring device at arbitrary voltage and temperature, A. Shnirman, D. Mozyrsky and I. Martin, Europhys. Lett. 67, 840 (2004).

We have accomplished a quantitative theory of the quantum dynamics of Andreev level qubits. This is a new type of super-conducting flux qubit where the switching between the two persistent current states in a SQUID is achieved by employing a true microscopic system formed by the two-level Andreev bound states in a super-conducting atomic-size quantum point contact (QPC) embedded in the SQUID (see the figure above). In this Andreev level qubit (ALQ), the quantum information is stored in the microscopic quantum system; the Andreev bound states, similar to non-super-conducting solid-state qubits like localized spins on impurities or quantum dots. Read-out of the Andreev level qubit is achieved by monitoring the macroscopic persistent current or the induced flux in the SQUID, similar to the conventional flux qubits. The essential difference between the ALQ and conventional flux qubits based on the phenomenon of macroscopic quantum coherence (MQC) is that its operation requires almost transparent Josephson junctions, while MQC qubits employ tunnel junctions. Furthermore, the ALQ dynamics involves two interacting, bosonic and fermionic, quantum fields: the super-conducting phase, and the two-level Andreev system (in MQC qubits only super-conducting phase is important). This difference made it necessary to reconsider and substantially extend the "orthodox" MQC theory. This is done by incorporating exact boundary condition for the junction in the Feynman path integral describing the qubit dynamics. During time evolution of the Andreev levels, the current through the QPC changes, and the QPC operates as a quantum switch, which controls the direction of the circulating current in the SQUID. To maintain the current switching, the intrinsic dynamics of the current in the SQUID must be sufficiently fast. Fidelity of read out of the Andreev level state by performing quantum measurement of the circulating current, or of the corresponding induced flux, requires the Andreev energy to be small compared to the plasma frequency of electromagnetic fluctuations. To prevent dissipation, both the Andreev level energy and plasma frequency must be small compared to the super-conducting energy gap. These inequalities determine the window of the circuit parameters where the ALQ operates. They are consistent with typical parameters of the flux qubit circuits. Strong interaction of the Andreev levels in QPC with plasma oscillations gives rise to effective suppression of generic contact reflectivity; hence, the Andreev level energy and therefore the frequency of the qubit operation can be controlled by varying the circuit parameters. The interaction between ALQs is achieved via inductive coupling of the qubit SQUIDs, providing an effective qubit Hamiltonian including qubit-qubit interaction. To investigate the relaxation and dephasing of ALQ, we have also considered the interaction of Andreev levels with phonon modes in the superconductor, and derived the corresponding kinetic equation. Evaluation of the relaxation and dephasing rates have shown that the phonon mechanism does not impose any further limitations on the qubit operation compared to the common for flux qubits dephasing mechanisms such as external flux fluctuations, and qubit radiation. ALQ theory is a general theory for the quantum behaviour of highly transparent Josephson junctions. Several aspects of the ALQ are important for all flux qubits. This concerns first of all the mechanism of qubit interaction with the circuit plasma modes. Another important aspect is the quality of the tunnel Josephson junctions employed for the MQC qubits: the presence of just few transparent conducting modes in the tunnel barrier may considerably affect the qubit behaviour, introducing the ALQ features, and large amount of such modes may severely dephase the qubit. The results of the work are summarized and detailed in our recent publications.

We have fabricated Single Cooper pair Boxes (SCBs) in close proximity to a Single Electron transistor operated in the radio Frequency mode (RF-SET). The SCB acts an artificial two level system i.e. a qubit, and the RF-SET acts as a read out device, which can measure the charge of the qubit and thus the state of the qubit. We can control the state of the qubit by applying fast rectangular pulses to an electrode, which is capacitively coupled to the qubit. By varying the duration of the pulses, we are able to manipulate the state of the qubit. Using this scheme we have been able to observe quantum coherent oscillations in the qubit and we have also been able to measure the relaxation and decoherence times of the qubit. We typically get values of 100ns for the relaxation time and up to 10ns for the decoherence time.

We have performed spectroscopic measurements on two coupled flux qubits consisting of small super-conducting loops interrupted by three Josephson junctions with a small junction capacitance. The qubit eigenstates correspond to super-positions of clockwise and anti-clockwise circulating currents. Because the basic states of these qubis are flux states they are very insensitive to charge noise. The qubits are coupled inductively, which results in an Ising type of interaction. By applying microwave radiation, one observes resonances due to transitions from the ground state to the first two excited states. The position of these resonances as a function of the magnetic field applied reveals the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance. The analysis makes clear that the spectroscopic data are fully consistent with the two-qubit Hamiltonian. This Hamiltonian, in turn, opens the possibility of well-chosen one and two-qubit operations that lead to controlled entanglement. The new results support the notion that super-conducting flux qubits can be used to study entanglement in macroscopic quantum systems and for the development of non-trivial two-qubit gates such as the controlled-not.

Dilution refrigerators are machines capable of reaching temperatures of a few mK; they are used for a variety of applications requiring ultra-low temperatures such as research in nanoelectronics, superconductivity and super-fluidity. They are available commercially at a price of around 200Keuros, depending on the model and vendor. We have designed and fabricated a new model of dilution refrigerator (Ymir) using in-house expertise in cryogenics and manufacturing. The main advantage that distinguishes our machine from the commercial ones is that it combines the high cooling power of large dilution refrigerators with a short operation time and low helium consumption. Ymir is designed to be inserted directly into regular 5" transport Dewars, unlike commercial refrigerators, which require cooling of the Dewar at each cycle. Several technical innovations have been also implemented. To optimise the space in the IVC, a single flat block of copper in which a relatively large hole has been drilled acts both as a pot and as a support plate. The still heater uses an original design: the heating resistor is outside the still, but the heat is transmitted directly to the He liquid through a coiled copper rod thermally isolated with Teflon and fixed in place by CuNi thin tubes. The merit of this design is that it avoids plastic-metal connections (a major source of leaks), thus the machine will be very robust. Finally, the refrigerator has five step heat exchangers in a configuration that allows for cold electronics and filters to be anchored in thermal contact but above the mixing chamber. The last step heat exchanger is the largest; it is placed in the middle of this configuration and it consists of four-sintered silver powder channels drilled in a copper cylinder. The gas handling system consists of mechanical (both He sealed and normal) and diffusion pumps, as well as a pumping cabinet that we have built ourselves. The mixture is 1/4 3He/4He and is kept in a 80l tank at about 0.6 barr. The refrigerator has been built and leak tested. As always in cryogenics, leak testing is the most tedious part of the fabrication process. At this stage, we have eliminated all the sources of leaks and we have performed a few successful cooling tests. The refrigerator is currently at the final development stage. What we need to do in the near future is fine-tuning the impedances and the mixture, and adding a Roots still pump. We intend to use this refrigerator for quantum computing experiments. Due to its low fabrication and operation cost, this machine is perfectly suited for laboratories, which cannot afford to buy a commercial model.

We develop super-conducting quantum bits (qubits) for a future quantum computer. Specifically, we focus on flux qubits. We have achieved coherent quantum dynamics and have successfully implemented strong coupling to a harmonic oscillator so that a single photon could be exchanged. Our research is long-term; potentially a quantum computer is more powerful than any conventional computer, for specific tasks. Super-conducting qubits may provide the route to a large scalable quantum computer.

Achieving quantum coherence has been the main obstacle for the operation of quantum bit circuits. Although it was clearly understood that decoupling the circuit from the outside world was essential, no systematic strategy was available to achieve this goal. The quantronium circuit is the first example in which such a strategy was used. Decoupling the qubit from the readout circuitry is the main problem in achieving good quantum because it provides an entry port for undesired noise, and because strong coupling is necessary at readout time. We have developed a general strategy based on operating the qubit at a working point where the transition frequency is stationary respectively to small changes in the control parameters, which results in an effective decoupling of the qubit from the readout circuitry. For the purpose of readout, the working point is then displaced. This key-strategy has been implemented in a modified Cooper pair box circuit called the quantronium because it behaves as an artificial atom. The readout is performed by measuring the switching of the readout junction after a bias current pulse. The effective critical current is modified by the current of the qubit state in a small loop. The qubit is manipulating using microwave pulses applied to the box gate. A coherence time of 500ns was measured using a two pulse Ramsey interference scheme. This corresponds to a quality factor of about 25000, which is at the time of writing the best achieved for a qubit circuit. The quantronium has been patented, including the key strategy to minimize decoherence. This method is now currently used by the project partners working with the Cooper pair box and with the flux qubit. The most important publications describing this result, and the corresponding patent granted, are given in the document list. Other publications on the quantronium have not been mentioned there, but are listed in the final report of the SQUBIT project.

In most of the implementations proposed so far quantum gates are obtained by varying in time in a controlled way the Hamiltonian of the individual qubits as well as their mutual coupling. An alternative design makes use of quantum geometric phases, obtained by adiabatically varying the qubits' Hamiltonian in such a way to describe a suitably chosen closed loop in its parameter space. Geometric quantum computation may offer considerable advantages since it may be intrinsically fault-tolerant. Area preserving errors do not change the accumulated Berry phases around a given closed loop in the parameter space and therefore will not affect one- and two-qubit gates. A first proposal to implement geometric quantum computation has been put forward theoretically and verified experimentally in NMR quantum computation. The possibility to measure Berry phases in super-conducting nano-circuits has been put forward in G. Falci et al. Nature 407, 355 (2000). The proposed set-up consists of a super-conducting electron box formed by an asymmetric SQUID, pierced by a magnetic flux and with an applied gate voltage. As in the conventional charge qubit, the device operates in the charging regime. When restricted to the space spanned by two charge states |0>, |1> differing by one Cooper pair, the Hamiltonian takes the form of a spin-1/2 in an external fictitious magnetic field pointing in an arbitrary direction. The possibility to have an asymmetric SQUID is crucial to perform non-trivial loops in the parameter space. Non-Abelian phases can also appear in the quantum dynamics of super-conducting nano-circuits, this is what was the result of this part of the work of the consortium. There are various interesting aspects associated with this analysis. In addition to their possible detection, which is intriguing by itself, the existence of non-Abelian holonomies in superconducting nanocircuits leads to a new scheme for adiabatic charge pumping and allows to implement solid state holonomic quantum computation. The adiabatic manipulation of degenerate subspaces and the degeneracy condition itself is non-trivial to achieve for an artificially fabricated device. In the work by Faoro et al. the network proposed to realize solid-state non-abelian quantum computation consists of three super-conducting islands each of which is connected to a fourth island. Gate voltages are applied to the three bottom islands via gate capacitances. Also in this case the device operates in the charging regime each coupling is designed as a Josephson interferometer (a loop interrupted by two junctions and pierced by a magnetic field). Thus the effective Josephson energies can be tuned by changing the flux in the corresponding loop. Electrostatic energies can be varied by changing the gate voltages. One-qubit operation can be performed by changing the magnetic fluxes adiabatically. In some particular case, this adiabatic manipulation corresponds to a charge pumping between different parts of the super-conducting nano-circuit. When the two qubits (realize with the network described above) are connected via a Josephson junction, it is possible to realize a two-qubit operation as well. Some caution is required to apply this scheme. In an experimental realization it will be difficult to achieve perfect degeneracy of all states. Thus the question is imposed to which extend incomplete degeneracy of the qubit states is permissible. The adiabatic condition requires the inverse operation time to be smaller than the minimum energy difference to the neighbouring states. There is another important constraint on the operational time. As the degenerate states are different from the ground state of the system, the time must not be too large in order to prevent inelastic relaxation. The work by Cholashinski, motivated also by the recent experiment with Josephson-junction system composed of two coupled charge qubits, consider a different design as a potential candidate for observation of quantum holonomies. As compared to the previous proposal, where the simplest two-dimensional holonomies, are constructed using four coupled charge qubits, there is a simplification since only two qubits are employed. Moreover the transformations are realized within a twofold degenerate ground state, rather than excited state. In this way we avoid the problem of depopulation of the subspace, mentioned before, is alleviated. Assuming the perfect performance not affected by the noise one may rely on a quite simple design without strong constraints on the system parameters. Further studies in this second set-up require the implementation of two-qubit gates. Finally one may also use the device to study the process of the adiabatic charge transport.

Niobium is the material of choice for most scientific and industrial applications involving super-conducting metals, due its a relatively large critical temperature (9.26K compared to 1.175K of aluminium). The technology for producing large (micrometer scale) structures is well established; however, the fabrication of small super-conducting nano-structures using Nb as a material is a well-known difficult issue. The problem is that unlike aluminium, niobium belongs to the class of refractory materials, thus it is significantly more difficult to evaporate and deposit in a reliable way. We have developed a new technique for the nano-fabrication of small junctions; we have produced and measured structures such as single junctions and single-electron transistors. To prevent resist out-gassing, Nb is evaporated in a UHV chamber built in-house which has a large distance from the crucible to the sample holder; we have found the optimal evaporation and oxidation parameters for this configuration. For creating the junctions we use typically two-angle or three-angle shadow evaporation techniques. Using this method, we have fabricated single junctions, single electron transistors, and multiple junctions' structures with Nb only or with combinations of Nb and Al. All these structures have good well-defined IV characteristics and, once the optimal recipe was found, the sample fabrication failure rate was low (10-20%). The measurements on these structures allow us to extract information about the sub-gap density of states. We have also studied in detail a single electron transistor with Al leads and Nb island, which displayed interesting transport phenomena such as Cooper pair resonances. This technology is relevant for super-conducting nano-electronics in general. In the particular case of quantum computing, it could be used for the read-out systems of the qubits and for fabricating flux qubits. The main advantage of our technology with respect to other nano-fabrication techniques involving Nb is simplicity. In the case of charge qubits, the initial expectation that Nb islands connected to Al leads would reduce the quasi-particle contamination has not been fulfilled. At this moment, there exists no fabrication technique for overcoming this problem; therefore more material-science oriented studies will be necessary.

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