Emergent Quantum Simulators

Quantum Simulation promises insight into quantum physics problems which are beyond the ability to calculate with conventional methods.  Conventional quantum simulators are built either using a ‘digital’ Trotter decomposition of the problem or by directly building the Hamiltonian in the lab and performing ‘analogue’ experiments.  I will present here a different approach, by which the model to simulate emerges naturally from a completely different microscopic Hamiltonian implemented in the lab. I will illustrate this in the example of the emergence of the Sine-Gordon quantum field theory from the microscopic description of two tunnel coupled super fluids [1] and in the emergence of Fermionic Pauli blocking in a weakly interacting Bose gas [2]. Special emphasis will be put on how to verify such emergent quantum simulators and how to characterize them.  Thereby I will present three tools: High order correlation functions and their factorization [1], the evaluation of the quantum effective action and the momentum dependence of propagators and vertices (running couplings, renormalization of mass etc ..) of the emerging quantum field theory [3], learning the emerging Hamiltonian [4], quantum field tomography that points to a new way to read out quantum simulators [5] and a novel approach to find the structure of the simulaed physics model agnostic from the data by machine learning [6]. Together they establish general methods to analyse quantum systems through experiments and thus represents a crucial ingredient towards the implementation and verification of quantum simulators. 

[1] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

[2] F. Cataldini et al. Phys. Rev. X 12, 041032 (2022)

[3] T. Zache et al. Phys. Rev. X 10, 011020 (2020) 

[4] R. Ott et al. Phys. Rev. Res. 6, 043284 (2024)

[5] M. Gluza et al., Communication Physics 3, 12 (2020)

[6] F. Møller et al., arXiv:2509.13821