79 p.
Quantum simulations consist in the reproduction of the dynamics of a quantum systemon a controllable platform, with the goal of capturing an interesting feature of the considered model. It is broadly believed that the advent of quantum simulators will represent a technological revolution, as they promise to solve several problems whichare considered intractable in a classical computer. Although there are strong theoretical bases confirming this claim, several aspects of quantum simulators have still to bestudied, in order to faith fully prove their feasibility. More over, the general question on which features of the considered models are simulatable is an attractive research topic,whose study would help to define the limits of a quantum simulator.In this Thesis, we develop several algorithms, which are able to catch relevant properties of the simulated quantum model. The proposed protocols follow a new concept named embedding quantum simulator, in which the simulated Schrodinger equation is mapped onto an enlarged Hilbert space in a nontrivial way. Via this embedding, weare able to retrieve, by measuring few observables, quantities that generally require full tomography in order to be evaluated. Moreover, we pay a special attention to the experimental feasibility, defining mappings which are space efficient, and do not require the implementation of challenging Hamiltonians. The presented algorithms are general,and they may be implemented in several quantum platforms, e.g. photonics, trappedions, circuit QED, among others.First, we propose a protocol which simulate the dynamics of an embedded Hamiltonian,allowing for the efficient extraction of a class of entanglement monotones. This is done using an embedding that is able to implement unphysical operations, as is the case of complex conjugation. The analysis is accompanied with a study of feasibility in a trapped-ion setup, which can be generalised to other platforms following similar computational models. Second, we propose an algorithm to measure n-time correlation functions of spinorial, fermionic, and bosonic operators, by considerably improving previous versions of the same result. We apply this protocol to the computation of magnetic susceptibilities, as well as to the simulation of Markovian and non-Markovian dissipative processes in a novel way, without the necessity of engineering any bath. All the proposed protocols are designed with a single ancillary qubit, minimising the needed experimental resources.We believe that embedding quantum simulators have a potential to become a powerful tool in the quantum simulation theory, since they pave the way for improving the flexibility of a quantum simulator in diferent experimental contexts.