## Lecture Topics and Background References

**Michael Stern (4-6 October) (2 lectures + 1 training session)**

- Introduction to Quantum circuits

- Experimental aspects of circuit QED.

** **

**Francesco Tafuri (4-6 October) (2 lectures + training session 5 October)**

*Abstract*

Quantum hardware is what transforms the novel concepts of quantum computation and communication into reality. The key challenge is to control, couple, transmit and read out the fragile stage of quantum systems with great precision, and in a technologically viable way. This course aims at illustrating some aspects of this key challenge in realizing quantum hardware and technology, focusing on superconducting quantum devices.

Lesson 1- Path to superconducting quantum devices

Lesson 2- Superconducting qubits: concept, design, technology and measurement

- G. Wendin, Quantum information processing with superconducting circuits: a review, Rep. Prog. Phys. 80 106001, 2017.

- P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019); https://doi.org/10.1063/1.5089550

- A. Blais, A. L. Grimsmo, S. M. Girvin, A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).

- X. Gua, A. F. Kockum, A. Miranowicz, Y. Liu, F. Nori, Microwave photonics with superconducting quantum circuits, Physics Reports 718–719, 1–102, 2017.

- F. Tafuri editor, Fundamentals and frontiers of the Josephson effect, (Springer, Berlin, 2019).

**Ramon Aguado (4-6 October) (3 lectures+1 training session)**

- Fundamentals of Majoranas in condensed matter: from the Dirac to the Majorana equation, p-wave superconductors and the Kitaev model.

- Topological superconductivity in realistic implementations: Fu and Kane proposal with topological insulators, Rashba semiconductors, etc.

- Detecting Majoranas in condensed matter: basic protocols, state of the art, recent controversies of Andreev versus Majorana, connection to Yu-Shiba-Rusinov physics in superconductors, etc.

The main reference is my Majorana review:

**R. Aguado, La Rivista del Nuovo Cimento ****40, 523 (2017****)**

Other References:

**-J. Alicea, Rep. Prog. Phys. ****75, 076501(2012****).**

**-Elliot&Franz, Rev. Mod. Phys. ****87, 137 (2015****).**

**-R. Aguado and L. Kouwenhoven, Physics Today June 2020.**

**-E. Prada et al, Nature Review Physics, ****2 (10), 575-594, 2020**

** **

**Felix Von Oppen (7-9 October) (3 lectures+1 training session)**

**Braiding, nonabelian statistics, Majorana qubits, quantum correcting codes**

Topics of the lectures (roughly divided into the three lectures):

- braiding and nonabelian statistics

- Majorana qubits, readout, and gate operations

- lattice gauge theory & quantum error correction

As for reading material, let's start with lecture notes/reviews:

* F. von Oppen, Y. Peng, F. Pientka

*Topological superconducting phases in one dimension*

Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School (2017)

* K. Flensberg, F. von Oppen, A. Stern

*Engineered platforms for topological superconductivity and Majorana zero modes*

Nature Reviews Materials (2021) https://doi.org/10.1038/s41578-021-00336-6

* F. von Oppen, Y. Oreg

*Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation*

Ann. Rev. Cond. Mat. Phys. **11**, 397 (2020)

**Maciej Lewenstein (8-9 October) (2 lectures + 1 training session)**

**Introduction to quantum information theory**

**Lecture 1) Introduction to entanglement theory**

- Bipartite entanglement
- Entanglement criteria and witnesses
- Quantum channels
- Entanglement in many body systems: area laws
- Tensor networks
- Resource theories of entanglement, coherence...

**Lecture 2) **

- Recap – Entanglement theory
- Non-locality – crash course
- Non-locality as a resource
- Bell correlations in many body systems

- M. Lewenstein, A. Sanpera, and V. Ahufinger, “Ultracold atoms in Optical Lattices: simulating quantum many body physics”, 460 pages, Oxford University Press, Oxford, 2017, corrected paperback reprint ISBN 978-0-19-878580-4
- J. Tura, A. B. Sainz, T. Grass, R. Augusiak, A. Acín, and M. Lewenstein, Entanglement and Nonlocality in Many-Body Systems: a primer, a lecture for Varenna School 2014, arXiv:1501.02733; Proceedings of the International School of Physics “Enrico Fermi", Course 191 “Quantum Matter at Ultralow Temperatures”, edited by M. Inguscio, W. Ketterle, S. Stringari and G. Roati, (IOS, Amsterdam; SIF, Bologna) 2016, p. 505, arXiv:1501.02733

*Seminar*

*Seminar***Emanuele Dalla Torre (6 October)**

**Quantum simulations with quantum computers on the cloud**

ABSTRACT

Quantum computing holds the promise to solve specific computational problems much faster than any known classical algorithm. Current quantum computers are, however, too small and too noisy to perform useful calculations. In this talk I will follow a different route and show how to use these systems to study fundamental physical questions, and specifically those related to the dynamics of many-body quantum systems. I will focus on two specific applications of quantum computers on the cloud: the demonstration of the topological property of spin models [1] and the realization of a quantum system with long range interactions [2]. These works raise new basic questions concerning the effects of classical noise on quantum states of matter, and provide a useful benchmark for actual quantum computers.

REFERENCES

1. Daniel Azses, Rafael Haenel, Yehuda Naveh, Robert Raussendorf, Eran Sela, Emanuele G. Dalla Torre, Identification of symmetry-protected topological states on noisy quantum computers, Physical Review Letters 125, 120502 (2020)

2. Mor M. Roses, Haggai Landa, Emanuele G. Dalla Torre, Simulating long-range hopping with periodically-driven superconducting qubits, https://arxiv.org/abs/2102.09590