Emergent Quantum Simulators

Abstract

Quantum Simulation promises insight into quantum physics problems which are beyond the ability to calculate with conventional methods. Quantum simulators can be 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. 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], first attempt on learning the emerging Hamiltonian, and quantum field tomography that points to a new way to read out quantum simulators [4]. 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. As an example, I will report on the verification of the area law of mutual information [5] in a quantum simulation of a continuous QFT.