1. Final Report Summary - HYBMQC (Macroscopic quantum dynamics and coherence in hybrid superconducting circuits for quantum computation)

Abstract: Dr Longobardi carried out his research activity from 1 October 2009 to 30 June 2011 within the framework of the project 'Macroscopic quantum dynamics and coherence in hybrid superconducting circuits for quantum computation', which was funded under the Marie Curie Reintegration Grant (RG) of the European Commission's Seventh Framework Programme (FP7-PEOPLE, 2009, RG number 248933).

The main objective of the three years' project was to demonstrate the feasibility of a qubit of sufficient quality to form the building blocks of a quantum information hybrid technology, partly based on the Josephson effect in High Tc superconductors (HTS).

The project had several intermediate milestones distributed within the three years, ranging from time flight measurements on different types of junctions to the study of dissipation in various systems and specifically in HTS junctions. The main responsibilities of Dr Longobardi were to design various experiments aiming towards the final target, implement the experimental setup to perform quantum measurements and carry out measurements. He benefited from the experience and active collaboration of all members of the hosting group to design and realise the samples and, for the background on HTS, from two students, of PhD and undergraduate level, who worked with him during the course of the project. Moreover, the fellow benefited from a series of international collaborations of the hosting group on the themes of the project.

For important personal reasons Dr Longobardi preferred to move back to the United States of America and the project was interrupted at half time of its whole duration. The project could however be considered very successful in the sense that:
1. significant results and most of intermediate targets were achieved. This could was emphasised by the scientific report and the list of manuscripts which were already published or were in preparation by the time of the project interruption.
2. Dr Longobardi completed, during this Marie Curie experience, important steps forward for setting his scientific career. This was also documented by his new academic position in the United States of America.
3. Dr Longobardi acquired experience on novel topics of solid state physics and transferred his knowhow in quantum measurements on superconducting Josephson junctions (JJs) to young students.

The first step was the implementation of the experimental setup for measurements down to 20 mK. A third set of electronic filters was installed at the 50 mK stage to reduce noise during measurements and new electronics to perform switching current distribution measurements were installed and optimised. This equipment formed a solid platform to perform the necessary transport measurements.

At the same time we carried out systematic measurements both on low (LTS) and high (HTS) critical temperature superconductors' JJs. LTS firstly served to calibrate the new setup. We then focussed on special LTS JJs, i.e. on NbN / MgO / NbN with MgO barriers of about 1nm, characterised by very low values of the critical current density down to 3 A/cm2. NbN might present some advantages with respect to Nb junctions for the realisation of superconducting qubits, because of possible reluctance to form intrinsic two level systems, and was a reference system for HTS JJs as well. They demonstrated both relatively short fast non-equilibrium electron-phonon relaxation times and higher gap values, when compared with traditional junction technologies based on niobium (Nb), aluminium (Al) and lead (Pb). More importantly in our project, they were characterised by Moderately damped regime (MDR) in analogy to HTS JJs. The moderately damped nature of these junctions generated a characteristic diffusive phase dynamics, analogous to what happened in HTS JJs. This regime was quite distinct from the well known case of underdamped systems, for which Q was larger than 10, and apparently quite common in junctions characterised by low critical currents (Ic). Thermal fluctuations assisted in premature switching into the resistive state and, on the other hand, helped in retrapping back to the superconducting state. In view of a more and more relevant use of nanotechnologies in quantum superconducting electronics, and therefore of low values of Ic, studies on MDR could offer novel insights on dissipative effects on JJs and inspire appropriate designs to respond to specific circuit requirements. For these NbN junctions, a physical picture of moderately damped junctions emerged, with a damping substantially independent of the frequency and able to sustain macroscopic quantum tunnelling at lower temperatures.

Switching current probabilities were measured down to 20 mK for different HTS JJs. Junctions were in particular Yttrium barium copper oxide (YBCO) Grain boundaries (GBs), and different configurations characterised by a variable orientation of the interface with respect to the electrodes were explored. The GB forming the barrier changed as a function of the interface orientation and determined different barrier transparency and levels of dissipation. Apart from canonical quantum and thermal regimes, we found evidence of a tuneable moderately damped regime. HTS JJs seemed to offer complementary functionalities when compared to LTS systems, along with some more flexibility in tuning the crossover temperature of the phase diffusion regime.

The comparative analysis of LTS and HTS systems allowed to draw some relevant conclusions on the dynamical junction parameters, which determined MDR, as well as to better define the fingerprints of MDR. A change in the sign of the derivative of the second moment of the distribution at a turn-over temperature T and a modification of the shape of the distributions at temperature around T, which could be parameterised by the skewness, proportional to the third central moment of the distribution, were robust signatures of the phase diffusion regime.

The possibility to master YBCO GB junctions on the scale of hundreds of nm using both a 'classical' top-down approach and an intrinsic self-assembling of nano-channels, was important in order to achieve the necessary level of accuracy in the control of the structures to carry out a systematic analysis. Switching current spectra vice versa turned to demonstrate unique fingerprints of characteristic transport quantum modes in these systems. The fingerprints were also unique from a morphological point of view.

HTS JJs seemed to offer complementary functionalities when compared to LTS systems and more flexibility in tuning the crossover temperature of the phase diffusion regime, despite the presence of additional sources of dissipation that were still to be completely defined. The Q dissipation factor was, by the time of the project completion, not much higher than 10. We expected that higher Q values, and therefore lower levels of dissipation, could be achieved for biepitaxial junctions, when the GB width would be reduced to the size of a single facet, of the order of 100 to 200 nm, with the current limit for the width being approximately 500 nm.

Numerical codes were developed to support the conclusions of the experimental measurements. Most of results on NbN / MgO / NbN junctions were already published during the course of the project, while the manuscripts on switching current measurements on YBCO junctions were in progress.

Progress in the control of the properties of HTS GB JJs and a better understanding of their dynamical parameters allowed for the design of a HTS Superconducting quantum interference device (rf-SQUID), aimed to be on a longer time scale the cell of the HTS qubit. The use of the superconducting loop where the junction was embedded guaranteed to reach a further level of isolation from direct bias lines. In this way the bias could be executed by simply inductively coupling an on-chip superconductive coil to the qubit. The first design with fully high Tc superconductive technology was also the basis to move on to the hybrid structure.

Significant steps were also made on the realisation of hybrid structures. By the time of the project completion we had fully integrated and hybridised YBCO cells with InAs nanowires, which worked as barriers. Nanowires were of InAs and the final structure was technologically quite demanding due to the structural complexity of both components of the junctions. The fabrication process could be applied to all sorts of barriers and hybrid structures and paved the way to LTS / HTS hybrid devices able to match a wide range of demand of quantum superconducting electronics.

Overall, the work realised by Dr Luigi Longobardi within the framework of the Project 'Macroscopic quantum dynamics and coherence in hybrid superconducting circuits for quantum computation', which was funded by the European Commission's Seventh Framework Programme's Marie Curie Reintegration Grant number 248933 and partly supported by projects already active in the hosting group on related topics, had some impact on the possibility to use novel superconducting quit cells in nano-circuits. The efficiency that was clearly demonstrated for superconducting qubits based on classical junctions platforms could be partially extended to novel materials with possible novel functionalities.

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