Quantum fluctuators for simulating continuous quantum systems by discrete ones

Classical simulation of quantum many-body systems is usually very inefficient with long running times and high needs for memory (e.g., it is not even possible to store classically the arbitrary state of 50 qubits). One might overcome these difficulties by using other quantum systems, similar to the one we want to study, as quantum simulators. Most of the efforts in this direction has been concentrated on simulating discrete quantum systems (e.g. spin chains) with other ones that are relatively easy to prepare in the lab (ion traps, atoms in optical lattices, etc.). In this talk, I treat a different problem: How can we simulate a continuous quantum system (e.g. a QFT) with a discrete one? In particular, I show how (and in which sense) one can use the global quantum fluctuator observables of a discrete lattice system to store continuous quantum information. Finally, the question of how the stored state of a light field can be processed by operations on the discrete system is considered.