PhD program in Quantum Technologies 2019 Summer School

In the continuous variables (CV) approach, universal computation can be identified via a universal set of Hamiltonians, able to generate any arbitrary evolution as a combination of finite-time Hamiltonian unitaries, including Gaussian and non-Gaussian interaction - which are not easy to realise in an optical implementation. Differently form the discrete variables (DV) approach the two-modes entangling gate in the CV encoding is a Gaussian gate which can be implemented by combination of squeezing and linear optics. This has as consequence that the CV approach is particularly suitable for the one-way model of quantum computing based on cluster state. I will revise experimental generation of multimode quantum states for CV protocols and in particular the one based on optical frequency combs and parametric processes. The protocols, along with mode selective and multimode homodyne measurements, allow for the implementation of reconfigurable entanglement connections between the involved. This can be exploited for fabricating entanglement structures with regular geometry as cluster states or graphs with more complex topology which can emulate quantum physical systems in complex structures or quantum protocols in complex networks. I will also revise non-Gaussian operations, which are necessaries to reach a form of quantum advantage in this scenario

I will introduce some elements of adiabatic quantum computing, with special focus on approaches that aim to solve hard combinatorial optimization problems via quantum annealing. The main features of currently commercialized quantum annealing devices will be described.
I will provide some notions concerning quantum Monte Carlo algorithms and discuss how these simulation techniques are being use as a benchmark for quantum annealers and as a tool to inspect if and when a quantum quantum annealing devices might display a quantum speed-up compared to classical optimization methods.

I will introduce the basic concepts and provide real experimental examples of quantum state engineering and measurement, with special emphasis to continuous-variable quantum optical states of light. The first lecture will introduce fundamental ideas and describe the basic tools, such as parametric down-conversion processes and balanced homodyne detection, for the manipulation and complete characterization of a quantum light field. The second lecture will be devoted to presenting some advanced applications to a variety of nonclassical states of light, with illustrations of the most fundamental concepts of quantum mechanics at play in the laboratory.

Superconducting Nanowire Single-Photon Detectors (SNSPD) are very interesting for their overall performances in terms of system quantum detection efficiency, high maximum counting speeds achieved at wavelengths up to near-IR, ultra low darkcounts and very short jitter times.In this lesson we'll present the operation principle of SNSPDs, the fabrication processes and the various approaches followed for both optical coupling and electrinic read-out. The use of SNSPDs in some quantum applications will be also presented and discussed.

I will introduce some elements of adiabatic quantum computing, with special focus on approaches that aim to solve hard combinatorial optimization problems via quantum annealing. The main features of currently commercialized quantum annealing devices will be described.
I will provide some notions concerning quantum Monte Carlo algorithms and discuss how these simulation techniques are being use as a benchmark for quantum annealers and as a tool to inspect if and when a quantum quantum annealing devices might display a quantum speed-up compared to classical optimization methods.

I will introduce the basic concepts and provide real experimental examples of quantum state engineering and measurement, with special emphasis to continuous-variable quantum optical states of light. The first lecture will introduce fundamental ideas and describe the basic tools, such as parametric down-conversion processes and balanced homodyne detection, for the manipulation and complete characterization of a quantum light field. The second lecture will be devoted to presenting some advanced applications to a variety of nonclassical states of light, with illustrations of the most fundamental concepts of quantum mechanics at play in the laboratory.

Quantum annealing is a branch of quantum computation aimed at solving optimization problems. The optimization problem is encoded in a quantum Hamiltonian, whose ground state is the wanted solution. Standard quantum annealing works as follows. The qubit system is prepared in the ground state of a simple Hamiltonian. Then, the qubits are evolved in time using a time-dependent Hamiltonian that, at the final time, coincides with the one used to encode the optimization problem. If the evolution is slow compared to the minimal level spacing, then the adiabatic theorem of quantum mechanics ensures macroscopic occupation of the target ground state at the end of the evolution.

The algorithm is limited by small spectral gaps, occurring in the presence of quantum phase transitions, and is realized in the presence of dissipation, due to the interaction with the environment. While disruptive in general, low-temperature environments can sometimes favor quantum annealing, improving the success probability. This beneficial effect can be further enhanced using pauses at specific times during the dynamics, favoring thermal relaxation towards the ground state.

My talk will present some results concerning quantum annealing in the presence of dissipation, with and without pauses, for the p-spin model, a prototypical Ising system often used as a benchmark for quantum annealing. This model is hardly studied experimentally due to its full connectivity and the presence of p-body interactions. However, its rotational symmetry allows for an easy numerical analysis in the weak coupling limit. I will show that dissipation and pauses can improve the success probability of the quantum annealing of this model.

Quantum annealing can be used to solve optimization prob-
lems. Quantum processors, performing quantum annealing, operate mini-
mizing a cost function. The central issue is to map the cost function which
has p-body interactions into a function with at most 2-body interactions.
In the already existing method of minor embedding, xing the number of
ancillae qubits for highly interacting models becomes impractical. Here
we propose a technique for obtaining approximate mapping based on ge-
netic algorithms. We verify the feasibility of this procedure by mapping
ferromagnetic p-spin model in two analytically solvable cases.

Based on the manuscript submitted to the journal of Quantum Machine Intelligence-
Passarelli, G. et. al, An evolutionary strategy for nding eective quantum 2-body
Hamiltonians of p-body interacting systems.

I review the most promising quantum algorithms and applications suitable for existing and near futures devices. I present results concerning proof-of-principle calculations on IBM hardwares ranging from combinatorial optimization (e.g. protein folding), electronic structure (e.g. chemistry and condensed matter), and sampling (useful for financial applications).

Ultracold atomic gases provide a formidable platform for quantum simulation of a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which accurate theoretical predictions are challenging even with state-of-the-art approaches. In this lecture, I will first briefly review the foundations of atom-light interactions and explain how these are exploited to cool, trap and manipulate atoms. I will then introduce ultracold atomic Fermi gases, from the non-interacting case to the famous strongly correlated BEC-BCS crossover. I will also describe some recent experiments, highlighting the unique and fascinating aspects of crossover superfluids. In the second part of the lecture, I will present a general introduction to the Fermi-Hubbard model and outline its realization with ultracold fermions in optical lattices, highlighting the foremost experimental achievements so far. To conclude, I will shortly discuss some novel approaches to quantum simulation of quantum magnetism and long-range interacting systems.

In this work we are going to study cavity optomechanical systems where the coupling between electromagnetic radiation and mechanical motion is considered. In this fast-growing field, the interaction of radiation field with the vibrational motions of a mechanical oscillator has many promising applications such as precision force sensing and evaluations of quantum physics at macroscopic scales. The standard and simplest optomechanical setup is a Fabry-Perot cavity in which one of the two mirrors is a vibrating micromechanical object. In fact, it has been the first experimentally studied cavity optomechanical system. It is also possible to place a mechanical element inside the optical cavity such as a flexible membrane which could be exploited for applications such as quantum detection of weak forces, displacements, masses, and accelerations. In this research, our main aim is to perform a quantum theoretical analysis on the power-noise spectrum by considering the phase measurements in a cavity optomechanics setup involving a coherently driven membrane in the middle of the cavity. In other words, mechanical motion of the system is studied by monitoring the phase of the optical cavity output.

We discuss the intimate connection between the quantum speedup of the (pseudo-)pure state Grover algorithm and the detection of multipartite entanglement using the Quantum Fisher Information (QFI). The quantum speedup is proportional to the maximal QFI during the algorithm, and hence proportional to the thereby detected k-partite entanglement. For small purities, speed-up still persists even though no entanglement is detected, however, the QFI still remains a quanfitier of the speed-up.

The Davydov model describes energy transfer in the hydrogen-bonded spines that stabilize protein α-helices. Its Hamiltonian has three parts: Ĥ =Ĥ ex+Ĥ ph+Ĥ int, where Ĥ ex is the exciton Hamiltonian (describing the internal amide-I excitations of the peptide groups), Ĥ ph is the phonon Hamiltonian (describing deformational oscillations of the lattice) and Ĥ int is the interaction Hamiltonian (describing the interaction of amide-I excitation with the motions of the lattice sites).
The primary goal of the thesis project is to go beyond the energy transfer and study the full state transfer along the α-helix by considering the Hamiltonian Ĥ as corresponding to a spin network.
Preliminary investigations on the phase dynamics, which only account for Ĥ ex, show the possibility of perfect state transfer between distant qubit.
We suspect however that the addition of Ĥ ph+Ĥ int can wash out the coherence, and we are currently estimating the time scale of this effect.
Subsequently, we will pursue the same goal by modifying the Davydov model. In particular, we plan to introduce physically motivated anharmonic terms in Ĥ ph and site-dependent coupling constants in Ĥ int. These could lead to coherence recovery and hence facilitate the quantum state transfer through the protein α-helices.

In the recent years van der Waals heterostructures (vdWHs) have received great interest, due to their physical properties and attractive applications in nanoelectronics and optoelectronics. These systems have an unprecedented number of degrees of freedom, such as number of layers, stacking order, interlayer distance, twist angle and so on. Tuning them significantly affects the electronic properties of the system, leading to a new “tuning-on-demand paradigm”, which highlights how vdWHs can be suitably used for the implementation of new electronic devices and quantum technologies. In this talk this paradigm is applied to vdWHs based on transition-metal dichalcogenides (TMDs). First principles calculations of the structural and electronic properties of these systems unveil the richness and tunability of such properties, providing a contribution to new electronic devices architectures and quantum emitter configurations for nanophotonics and quantum information applications.

References
- Felice Conte, Domenico Ninno, and Giovanni Cantele, Phys. Rev. B 99, 155429 (2019)
- Felice Conte, Domenico Ninno, and Giovanni Cantele, “Bands tuning in transition metal dichalcogenide heterostructures: the interplay between thickness and electric field” submitted

Quantum key distribution (QKD, or more generically, quantum cryptography) is today the sole technology able to guarantee unconditional security in sensitive data exchange, as QKD protocols are in principle effective regardless of the computational power available to a potential eavesdropper. Although QKD devices are already adopted outside the laboratories, this technology is still far from a large-scale deployment in existing fiber networks and telecom infrastructures, due to practical issues as low secret-key rate achievable, high costs and high requirements in terms of low-noise fiber links. These practical challenges in experimental QKD are the main topic of my talk. Indeed, my PhD project is focused on QKD in-field demonstrations, with the aim of proving its compatibility with already installed fiber links, while also testing its robustness against classical signals co-propagating through the same fiber. Specifically, I will address two QKD field-trials involving a metropolitan fiber channel in Florence and a submarine fiber link between Sicily and Malta. In addition, I will show the results of my collaboration with Technical University of Denmark, in which we set up a prototype for high-dimensional QKD, with the aim of increasing the secret-key rate achievable while maintaining a cost-effective experimental apparatus.

Since its theoretical prediction in 1962 [1], the tunnelling current (with no applied voltage) that arises in a system constituted by two superconductors separated by a barrier has been the subject of many scientific studies. It was quite soon discovered that the current-phase relation I=ICsin(ϕ) (where ϕ is the phase difference between the order parameter of the two superconductors) as predicted in [1] does not always apply, depending both on the temperature and the barrier of the system. As a matter of fact, quite different types of current-phase relation can be found using as the separating barrier either insulators, normal metals, and superconductors, or more general constrictions of different heights and widths both in condensed matter and in ultra-cold atoms experiments.

In order to better understand the mechanism at the basis of the DC Josephson effect and to model both the current-phase relation and the critical value IC, several theoretical and numerical approaches have been developed. The early works relied mostly on the Ginzburg-Landau equations [2][3][4][5][6], but there were also attempts to use microscopic theories [7][8][9] or perturbative calculations [10]. More recently methods have been developed based on the quasi-classical Green’s functions [11][12] and the Bogoliubov-deGennes (BdG) equations [13][14].
Despite some good agreements with the experimental data [15][11][12], none of these approaches could be successfully applied to the following circumstances of physical interest:

over the whole temperature range from T=0 to T=Tc;
to all possible barrier widths and heights;
along (most part of) the BCS-BEC crossover.

The main reason underlying of our study of the DC Josephson effect has been to fill this gap. To this end, we have made use of a local-phase-density approximation to the BdG equations, both in its local (LPDA) [16] and non-local (NLPDA) [17] versions. Both LPDA and NLPDA approaches, which are computationally faster and less storage demanding than the BdG equations, give us the opportunity to study the behavior of the Josephson current with reliable results along the BCS side of the BCS-BEC crossover, with no limitations on the barrier width and down to low temperatures.

REFERENCES:

[1] B.D. Josephson. Possible new effects in superconductive tunnelling.
Physics letters, 1(7):251–253, 1962.

[2] P. De Gennes. Self-consistent calculation of the josephson current. Phys.
letters, 5, 1963.

[3] P. de Gennes. Boundary effects in superconductors. Reviews of Modern
Physics, 36(1):225, 1964.

[4] H.J. Fink. Supercurrents through superconducting-normal-superconducting
proximity layers. i. analytic solution. Physical Review B, 14(3):1028, 1976.

[5] H.J. Fink and RS Poulsen. Supercurrents through proximity layers. ii. numeri-
cal solution of superconducting-normal-superconducting and superconducting-
superconducting-superconducting weak links. Physical Review B, 19(11):5716,
1979.

[6] A. Baratoff, J.A. Blackburn, and Brian B Schwartz. Current-phase
relationship in short superconducting weak leans. Physical Review Letters,
25(16):1096, 1970.

[7] L. Aslamazov,A. Larkin, Yu N Ovchinnikov, and Z Fiz. Josephson effect in
superconductors separated by a normal metal. Sov. Phys. JETP, 28(1):171,
1969.

[8] I.O. Kulik. Macroscopic quantization and the proximity effect in sns junctions. Soviet Journal of Experimental and Theoretical Physics, 30:944, 1969.

[9] J. Bardeen and J.L. Johnson. Josephson current flow in pure
superconducting-normal-superconducting junctions.Physical Review B,5(1):72, 1972.

[10] V. Ambegaokar and A. Baratoff. Tunneling between superconductors.
Physical Review Letters, 10(11):486, 1963.

[11] F.K. Wilhelm, A.D. Zaikin, and G. Schön. Superconducting current
in narrow proximity wires. Czechoslovak Journal of Physics, 46(4):2395–2396,
1996.

[12] P. Dubos, H. Courtois, B. Pannetier, F.K. Wilhelm, A.D. Zaikin, and G. Schön.
Josephson critical current in a long mesoscopic sns junction. Physical Review
B, 63(6):064502, 2001.

[13] A. Spuntarelli, P. Pieri, and G. Calvanese Strinati. Solu-
tion of the bogoliubov–de gennes equations at zero temperature throughout
the bcs–bec crossover: Josephson and related effects. Physics Reports, 488(4-
5):111–167, 2010.

[14] G. Watanabe, F. Dalfovo, L.P. Pitaevskii, and S. Stringari.
Effects of periodic potentials on the critical velocity of superfluid fermi gases
in the bcs-bec crossover. Physical Review A, 83(3):033621, 2011.

[15] C.S. Lim, J.D. Leslie, H.J.T. Smith, P. Vashishta, and J.P. Carbotte. Temperature variation of the dc josephson current in pb-pb tunnel junctions. Physical Review B, 2(6):1651, 1970.

[16] S. Simonucci and G.C. Strinati. Equation for the superfluid gap obtained by
coarse graining the bogoliubov–de gennes equations throughout the bcs-bec
crossover. Phys. Rev. B, 89:054511, Feb 2014.

[17] S. Simonucci and G. Calvanese Strinati. Nonlocal equation for the supercon-
ducting gap parameter. Phys. Rev. B, 96:054502, Aug 2017.

Spintronics and Quantum Electronics represent the new candidates for future high-performance computer and information processes. The use of the electron spin, rather than charge, as information carrier, can for instance define the unit of quantum information: the quantum bit (qubit). Recent developments have shown that the exploitation of the Rashba Spin Orbit Coupling (SOC) in two-dimensional (2D) materials is an innovative and attractive solution for the quantum computation. For example, SOC is used for a more efficient charge to spin conversion in spin-orbit torque devices.
Here we propose two-dimensional oxide (2D-oxides) systems as innovative quantum devices 1. The idea is to combine Rashba spin-orbit coupling (SOC), 2D-magnetism, superconductivity (SC) and high-mobility in the same 2D electron gas (2DEG) that is formed at the interface between wide bandgap insulators oxides. We have demonstrated that the superconducting 2DEG created at the interface between LaAlO3 and SrTiO3 (LAO/STO) becomes spin polarized by introducing a few unit cells of delta doping EuTiO3 (ETO), an antiferromagnetic (AF) insulator iso-structural to STO 2. Firstly, we have investigated the interplay between ferromagnetism and Rashba spin-orbit interactions by studying the magnetoconductance curves of the 2DEG as a function of the applied gate voltage and temperature 3. Recently we have also found that the interface exhibits, under visible light, a persistent photoconductivity and anomalous Hall effect. This feature is probably related to the different nature of the photo-excited spin-polarized 4f carriers due to ETO.
The application of oxide 2DEGs to advanced electronics requires also the creation of suitably designed nanodevices. We have realized (LAO/STO) tunnel devices using Helium focused ion beam (He-FIB). Our preliminary measurements show that these devices are fully tunable and could have interesting tunnel I-V characteristics. Our results show that these oxide nanodevices could have a significant and far-reaching impact for new quantum spintronic development.

Hybrid mesoscopic systems in which conventional superconductivity, spin-orbit interactions, and magnetism come into play at the same time, have attracted a lot of interest in recent studies, allowing for the possibility to carry, manipulate and transform quantum information, which is a great advantage to develop components for applications in quantum technology.
In particular, superconducting circuits with Josephson junctions are among the leading candidates for the realization of the fundamental building blocks of a quantum computer.
In this context, we present a study concerning the anomalous Josephson effect [1], predicting a finite pair current in the absence of phase difference between the superconductors.
We focus to S/SO/F/S system in which spin-orbit coupled and ferromagnetic layers alternate. We calculate the Josephson current carried by the subgap Andreev levels calculated as a function of the phase difference φ between the two superconductors, using a scattering matrix formalism, based of phenomenological scattering matrices. We show that the coexistence of spin-orbit interaction and Zeeman effect is sufficient to break spin rotation and time-reversal symmetry in spatially separated regions of the junction, allowing to observe an anomalous Josephson effect. We also show that in the presence of an anomalous phase shift, a direction dependent critical current can show up.
Finally, future perspectives of our work will be discussed, such as a semi-empirical microscopic description of the superconducting proximity effect, where the transport properties of the system are studied using the recursive Green’s functions method on a two- dimensional Bogoliubov De Gennes tight-binding Hamiltonian.

References:
[1] M. Minutillo, D. Giuliano, P. Lucignano, A. Tagliacozzo, and G. Campagnano, Phys. Rev. B 98, 144510 (2018).

The ideal quantum Zeno effect is a robust method to protect the coherent dynamics of a quantum system. In particular, in the weak quantum Zeno regime, repeated quantum projective measurements can allow the sensing of semi-classical field fluctuations.
In this talk I will show our proposal and demonstration, both theoretical and experimental, of a novel noise-sensing scheme enabled by the weak quantum Zeno regime. We experimentally tested these theoretical results on a Bose-Einstein Condensate of 87Rb atoms realized on an atom chip, by sensing ad hoc introduced noisy fields.

In this work we present a study on the dark counts rate in a NbTiN
Superconducting Nanowire Single Photon Detectros (SNSPD). The strip is 80nm wide, hence
we are in the 2D regime. We measure the distribution of the time intervals elapsed between two
consecutive dark pulses at 4,2K and we do not observe a simple Poisson distribution as expected
but a combination of two Poisson-like processes, occurring with two dierent rates. The two
measured dark counts rate exhibit a dierent dependence on the bias current: one process
dominates at lower bias and the other bocomes more prominent as the current increases. In
the scenario presented by Ejrnaes et al. [1], this result could conrm that, in this temperature
regime, dark counts are generated mainly by multiple consecutive
uctuation events. The result
can also be a footprint of two dierent process occurring in the nanostrip.

References
[1] Ejrnaes M, Salvoni D, Parlato L, Massarotti D, Caruso R, Tafuri F, Yang X Y, You L X, Wang Z, Pepe G P and Cristiano R 2019 Scientific Reports 9 8053

This lecture considers a Josephson junction in series with an impedance voltage biased below the gap. In this simple quantum electrodynamics system, the coupling constant between Cooper pair tunneling and each mode of the impedance is determined by the ratio between the mode impedance Z=√(L/C) and the relevant resistance quantum RQ= h/(2e)2 ~6.5 kOhms. A series of interesting situations that have been investigated will be considered in this lecture.
In the simplest case of a single mode resonator, the transfer of a single Cooper pair only occurs when its energy 2eV can be transformed in 1,2,..n photonic excitations in the resonator. This inelastic tunneling phenomenon is the essence of Dynamical Coulomb Blockade. In the strong coupling regime, the presence of a single photon can even block the creation of a second one, which forces the resonator to emit a single photon in the external circuit before another Cooper pair can pass and re-excite it. One gets this way a very simple single photon source.
In a two-mode resonator circuit with different frequencies, the transfer of a single Cooper pair can simultaneously excite a single photonic excitation in each mode. The photons leaking out of the resonators in the measurement lines are then entangled. In the particular case of two resonators respectively with a high (low) Q, the stabilization of a single excitation Fock state in the high Q resonator can furthermore be achieved.
Applications are sought for these non-classical sources of radiation in the microwave domain that could be extended up to the THz frequency range.

Ultracold atomic gases provide a formidable platform for quantum simulation of a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which accurate theoretical predictions are challenging even with state-of-the-art approaches. In this lecture, I will first briefly review the foundations of atom-light interactions and explain how these are exploited to cool, trap and manipulate atoms. I will then introduce ultracold atomic Fermi gases, from the non-interacting case to the famous strongly correlated BEC-BCS crossover. I will also describe some recent experiments, highlighting the unique and fascinating aspects of crossover superfluids. In the second part of the lecture, I will present a general introduction to the Fermi-Hubbard model and outline its realization with ultracold fermions in optical lattices, highlighting the foremost experimental achievements so far. To conclude, I will shortly discuss some novel approaches to quantum simulation of quantum magnetism and long-range interacting systems.

In this series of lectures I will describe how superconducting transmon
qubits are engineered, designed, and fabricated.

I start introducing the building blocks of superconducting quantum
processors from an engineering point of view, with a focus on working
parameters and design considerations. I will emphasize similarities with
standard microwave engineer elements such as transmission lines,
resonators, and capacitive or inductive couplings.

I will provide a deep insight on how the working parameters of the quantum
processor are linked to the performances of the device and to the lifetime
of the qubits.

I will conclude with an overview of the common fabrication techniques to
produce superconducting quantum processors.

At the end of this series of lectures the audience will be familiar with
equations and tools used to engineer superconducting transmon quantum
processors. Moreover, they will know how to balance the tradeoff between
performances and coherence times imposed at the design stage.

Building scalable Quantum Information Processing systems requires the ability to perform addressing, readout, control, addressing and signal distribution for individual quantum elements using low-power cryogenic devices co-located or integrated at the mK stage. We propose to accomplish this using a novel superconducting device - Symmetric rf-SQUID. This device has been successfully tested as the fundamental element of a Symmetric Traveling Wave Parametric Amplifier (STWPA), giving improved performances with respect to the existing TWPAs. Thanks to its flexibility, the Symmetric rf-SQUID allowed us to independently tune both even and odd nonlinear terms of the Josephson current-phase relation. Based on this behavior, we perform analytical and numerical simulations showing the possibility to operate the Symmetric rf-SQUID in many scenarios as rf up-down conversion mixers, tunable-unitary gain phase shifters and linear tunable inductances with an inductance-value-independent weak nonlinearity. The obtained results will be presented and discussed.

The continuous development of superconducting electronics is encouraging several studies on hybrid Josephson Junctions (JJs), such as SFS heterostructures. The competition between the superconducting order parameter in the electrodes and the ferromagnetic order parameter in the barrier leads to unconventional properties like: second harmonics in the current-phase relation (CPR), a transition in the phase difference between the electrodes from 0 to π and the formation of spin-triplet Cooper pairs currents, exploitable in spintronic devices and switchable elements in quantum/classical circuits. However, most of the applications of SFS JJs in real superconducting circuits are limited by the high decoherence in these devices due to quasiparticles poisoning. We propose here an electrodynamic characterization of a new kind of ferromagnetic JJs in which the barrier is an insulating ferromagnet (tunnel-ferromagnetic spin-filter JJs). Spin-filter JJs show evidences of MQT and an incomplete 0-π transition that could enhance the capabilities of SFS JJs also as active elements. In order to meet specific circuit requirements it is necessary a full comprehension of the dissipation processes and the knowledge of the scaling laws with the thickness of fundamental electrodynamics parameters, like the resistance due to the quasiparticles and the capacitance of the device. We show that the Tunnel Junction Microscopic (TJM) model leads to a reliable and self-consistent estimation of these parameters, and that our self-consistent approach can be fully extended to other type of tunnel JJs.

We show how to express fermionic problems in qubit language, exploring
different techniques. We then expose the limitations of current state
of the art quantum computers in solving correlated fermionic systems
such as molecular models.

In the domain of electrical circuits, superconducting quantum bits based on Josephson junctions are presently the most advanced qubits. I will describe the single Cooper pair box circuit, its transmon version used nowadays, and the operation of an elementary quantum processor. I will explain the scalability challenge required by quantum error correction, and the alternative routes for facing it. We are developing such an alternative hybrid route based on spins with superior quantum coherence coupled to quantum superconducting circuits. I will present the progress achieved in the control of a small number of electronic spins for performing ultra-sensitive Electronic Spin Resonance, and the perspectives open for quantum information processing.

In this series of lectures I will describe how superconducting transmon
qubits are engineered, designed, and fabricated.

I start introducing the building blocks of superconducting quantum
processors from an engineering point of view, with a focus on working
parameters and design considerations. I will emphasize similarities with
standard microwave engineer elements such as transmission lines,
resonators, and capacitive or inductive couplings.

I will provide a deep insight on how the working parameters of the quantum
processor are linked to the performances of the device and to the lifetime
of the qubits.

I will conclude with an overview of the common fabrication techniques to
produce superconducting quantum processors.

At the end of this series of lectures the audience will be familiar with
equations and tools used to engineer superconducting transmon quantum
processors. Moreover, they will know how to balance the tradeoff between
performances and coherence times imposed at the design stage.

Device-independent quantum information processing represents a new framework for quantum information applications in which devices are seen as black boxes processing classical information. In particular, no assumptions are made on the inner working of these devices except their quantum functioning. The lecture introduces the main ideas and tools of the device-independent scenario and argues why it is especially relevant for quantum cryptography applications.

We show how the use of neural networks can help augmenting the
precision of observables estimation on a quantum computer, addressing
one of the main challenges of short-depth algorithms.

Quantum programming languages have been introduced
about twenty years ago mainly from a theoretical
perspective. Nowadays, several efforts have been devoted to
the construction of real quantum architectures. We can
therefore map the theoretical findings into concrete
programming platforms.
In this lecture, we will introduce the notions at the basis of
high-level quantum programming and show some examples
of quantum programs by using existing platforms.

Quantum programming languages have been introduced
about twenty years ago mainly from a theoretical
perspective. Nowadays, several efforts have been devoted to
the construction of real quantum architectures. We can
therefore map the theoretical findings into concrete
programming platforms.
In this lecture, we will introduce the notions at the basis of
high-level quantum programming and show some examples
of quantum programs by using existing platforms.