Schedule

UNM Physics and Astronomy, Summer 2023 course

Quantum Internet:

1. Welcome to the Quantum Internet, and to the Science of Teaching!
   [Tzula] [April 27th]
2. Quantum Internet Overview: What is it good for and how can we build it?
   [Tzula] [May 4th]
3. Quantum Networks and Entanglement Distribution
   [Hariprasad Madathil & Robert Kramer] [May 31st]
4. Quantum Cryptography and Quantum Key Distribution
   [Juan Gonzalez de Mendoza & Alex Fischer] [June 7th]
5. Blind and Distributed Quantum Computation
   [Piper Wysocki & Evan Borras Blind] [June 14th]
6. Distributed Quantum Sensing and Hybrid Quantum Applications
   [Andrew Zhao & Spencer Dimitroff] [June 16th]

Quantum Metrology:

1. Mathematical Fundamentals for Parameter Estimation
   [Marco] [June 28st]
2. Quantum Fisher Information and Adaptive Estimation Schemes
   [Apollo & Mohsin] [July 12th]
3. Continuous Variable Quantum Parameter Estimation
   [Cole Kelson-Packer & Jalan Ziyad] [July 19th]
4. Parameter Estimation for Non-unitary Operations
   [Shravan Shravan & Ben Corbett & Cole Maurer] [July 26th]
5. Applications: Quantum Metrology and Quantum Sensing
   [Sudhan Bhadade, Andrew Frobes & Vikas Buchemmavari] [August 2nd]

Detailed Schedule

Quantum Internet

• Welcome to the Quantum Internet, and to the Science of Teaching! [Tzula] [April 27th]

The purpose of this introductory lecture is twofold. Firstly, to introduce the students to the goals of current quantum internet research activities. [1] Secondly, to introduce students to the science of teaching (and in particular, metacognition) which we will make use of as a guiding principle for learning and teaching throughout the course.

• Quantum Internet Overview: What is it good for and how can we build it? [Tzula] [May 4th]

In the second lecture, we will dive a little deeper into the applications of the quantum internet: in particular, distributed quantum computation, blind quantum computation, quantum cryptography including quantum key distribution, and distributed quantum sensing [2]. Then, we will discuss the general structure of a quantum network in terms of the hardware.

• Quantum Networks and Entanglement Distribution [Hariprasad Madathil] [May 31st]

This student-led talk will focus on the hardware of the quantum internet: quantum repeaters [3-5], quantum routers [6], and the software that optimizes entanglement distribution over a network [7-9].

• Quantum Cryptography and Quantum Key Distribution [Juan Gonzalez de Mendoza & Alex Fischer] [June 7th]

This student led talk will introduce the students to the key concepts of qvuantum key distribution [14-17] and quantum cryptographic schemes more generally [18, 19].

• Blind and Distributed Quantum Computation [Piper Wysocki & Evan Borras Blind] [June 14th]

This student-led talk will focus on quantum computation on the quantum grid [10] and, in particular, both the unique challenges associated with implementing quantum computing and error correction [11,12], and the unique advantages of distributed quantum computing such as blind computation [13].

• Distributed Quantum Sensing and Hybrid Quantum Applications [Alex Fischer & Spencer Dimitroff] [June 16th]

This student led talk will conclude our study of the quantum internet, and is left more free-form. Students are encouraged to discuss distributed quantum sensing [20], as well as any other potential uses of the quantum internet (e.g. clock synchronization [21], voting [22]) that do not fall into the above listed categories.

Quantum Metrology:

• Mathematical Fundamentals for Parameter Estimation [Marco]

This topic covers the essential mathematical concepts and techniques used in parameter estimation, with a focus on applications in the field of quantum mechanics. Topics may include probability theory, statistical inference, and numerical optimization methods. These techniques apply for classical and quatum systems [23,24].

• Quantum Fisher Information and Adaptive Estimation Schemes [Apollo & Mohsin]

This topic delves into the quantum Fisher information, which is a fundamental quantity in quantum parameter estimation that quantifies the sensitivity of a quantum system to small changes in its parameters [24,26]. The course may cover the mathematical foundations of quantum Fisher information, its connection to quantum metrology, and how it can be utilized in adaptive estimation schemes to optimize measurement strategies [24,25].

• Continuous Variable Quantum Parameter Estimation [Jalan Ziyad]

This topic focuses on parameter estimation for quantum systems with continuous variable degrees of freedom, such as quantum fields with bosonic modes [26]. It may cover techniques and methods for estimating parameters that describe continuous variable systems, including strategies based on Homodyne ang Heterodyne measurements. This topic is likely to be relevant in the context of quantum optics, quantum information processing, and quantum communication [27].

• Parameter Estimation for Non-unitary Operations [Shravan Shravan & Ben Corbett & Cole Maurer]

This topic deals with parameter estimation for quantum operations that are not unitary. In this problem, the aim is to estimate parameters that appears in quantum channels, which may introduce noise or decoherence into a quantum system [28,29].

• Applications: Quantum Metrology and Quantum Sensing [Sudhan Bhadade, Andrew Frobes & Vikas Buchemmavari]

This topic explores applications, such as magnetic field sensing, gravitational wave detection, or precision spectroscopy, and how parameter estimation techniques are employed in these contexts [29-31].

Bibliography

1. Kimble, H. The quantum internet. Nature 453, 1023-1030 (2008).
2. Stephanie Wehner et al., Quantum internet: A vision for the road ahead.Science362, eaam9288(2018).
3. Qiao Ruihong and Meng Ying 2019 J. Phys.: Conf. Ser. 1237 052032.
4. Azuma, K., Economou, S. E., Elkouss, D., Hilaire, P., Jiang, L., Lo, H. K., & Tzitrin, I. (2022). Quantum repeaters: From quantum networks to the quantum internet. arXiv preprint.
5. W. J. Munro, K. Azuma, K. Tamaki and K. Nemoto, "Inside Quantum Repeaters," in IEEE Journal of Selected Topics in Quantum Electronics, vol. 21, no. 3, pp. 78-90, May-June 2015, Art no. 6400813.
6. Lee, Y., Bersin, E., Dahlberg, A. et al. A quantum router architecture for high-fidelity entanglement flows in quantum networks. npj Quantum Inf 8, 75 (2022).
7. Kenneth Goodenough, David Elkouss, and Stephanie Wehner Phys. Rev. A 103, 032610.
8. K. Chakraborty, D. Elkouss, B. Rijsman and S. Wehner, "Entanglement Distribution in a Quantum Network: A Multicommodity Flow-Based Approach," in IEEE Transactions on Quantum Engineering, vol. 1, pp. 1-21, 2020, Art no. 4101321
9. Coopmans, T., Knegjens, R., Dahlberg, A. et al. NetSquid, a NETwork Simulator for QUantum Information using Discrete events. Commun Phys 4, 164 (2021).
10. J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello Phys. Rev. A 59, 4249
11. Qian Xu, Alireza Seif, Haoxiong Yan, Nam Mannucci, Bernard Ousmane Sane, Rodney Van Meter, Andrew N. Cleland, and Liang Jiang Phys. Rev. Lett. 129, 240502
12. Van Meter, R., & Devitt, S. J. (2016). Local and distributed quantum computation. arXiv preprint
13. Fitzsimons, J.F. Private quantum computation: an introduction to blind quantum computing and related protocols. npj Quantum Inf 3, 23 (2017).
14. Fang, XT., Zeng, P., Liu, H. et al. Implementation of quantum key distribution surpassing the linear rate-transmittance bound. Nat. Photonics 14, 422-425 (2020).
15. Diamanti, E., Lo, HK., Qi, B. et al. Practical challenges in quantum key distribution. npj Quantum Inf 2, 16025 (2016).
16. Peter W. Shor and John Preskill Phys. Rev. Lett. 85, 441
17. Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J. Cerf, Miloslav Dusek, Norbert Lutkenhaus, and Momtchil Peev Rev. Mod. Phys. 81, 1301
18. Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, and Hugo Zbinden Rev. Mod. Phys. 74, 145
19. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, "Advances in quantum cryptography," Adv. Opt. Photon. 12, 1012-1236 (2020)
20. Zheshen Zhang and Quntao Zhuang 2021 Quantum Sci. Technol. 6 043001
21. Shi, J., Shen, S. A clock synchronization method based on quantum entanglement. Sci Rep 12, 10185 (2022).
22. Xue, P., Zhang, X. A simple quantum voting scheme with multi-qubit entanglement. Sci Rep 7, 7586 (2017).
23. Keener, R. W. (2010). Theoretical statistics: Topics for a core course. New York: Springer.
24. Hayashi, M. (Ed.). (2005). Asymptotic theory of quantum statistical inference: selected papers. World Scientific.
25. Fujiwara, A. (2006). Strong consistency and asymptotic efficiency for adaptive quantum estimation problems. Journal of Physics A: Mathematical and Theoretical, 44, 079501.
26. Jing Liu et al 2020 J. Phys. A: Math. Theor. 53 023001
27. Stefano Olivares and Matteo G A Paris 2009 J. Phys. B: At. Mol. Opt. Phys. 42 055506
28. Sisi Zhou and Liang Jiang PRX Quantum 2, 010343
29. Geza Toth and Iagoba Apellaniz 2014 J. Phys. A: Math. Theor. 47 424006
30. Cohen, D., Gefen, T., Ortiz, L. et al. Achieving the ultimate precision limit with a weakly interacting quantum probe. npj Quantum Inf 6, 83 (2020).
31. Ziming Wang et al 2022 ApJ 932 102