Topic: Verification of quantum computation by randomized measurements
Group: Laboratoire de Physique et Modélisation des Milieux Condensés (LPMMC), Grenoble
Supervisor: Benoît Vermersch
Contact: benoit.vermersch@lpmmc.cnrs.fr
[bvermersch.github.io]

A central aspect for the future of quantum simulation and computation is the development of experimental tools to probe a new generation of many-body quantum states, which could not be realized so far. While standard measurement techniques give typically access to low-order correlation functions, accessing experimentally true quantum features, such as entanglement, was considered for many years as an outstanding challenge for quantum technologies. Recently, we have developed and demonstrated protocols known as randomized measurements (RM) [3,4], that have the potential to address this challenge.

The internship consists in implementing a verification protocol for quantum computers based on measuring the fidelity between two quantum states produced in two different devices [5]. This will be achieved by a numerical script, written in Python, that will allow us to interact with two IBM quantum devices. The goal will be to assess the fidelity of both devices, write a theory model to account for errors, and develop strategies for error mitigation. The code may be made publicly available and could be used in the future to benchmark other quantum systems.

This internship can be followed by a PhD (funding available)

References
[1] I. M. Georgescu, S. Ashhab, and F. Nori. “Quantum simulation”. Rev. Mod. Phys. 86 (2014), pp. 153–185.
[2] J. Preskill. “Quantum Computing in the NISQ era and beyond”. Quantum 2 (2018), p. 79 .
[3] A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller. “Rényi Entropies from Random Quenches
in Atomic Hubbard and Spin Models”. Physical Review Letters 120, 5 (2018).
[4] T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos. “Probing Rényi entanglement entropy via randomized measurements”. Science 364,6437 (2019), pp. 260– 263.
[5] Andreas Elben, Benoît Vermersch, Rick van Bijnen, Christian Kokail, Tiff Brydges, Christine Maier, Manoj K. Joshi, Rainer Blatt, Christian F. Roos, and Peter Zoller. Phys. Rev. Lett. 124, 010504 (2020).