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Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results allow us to assess the limits of the degree of quantum control attained in these kinds of experiments. The simulation of other physical systems, with different particle statistics, is also discussed.
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is b
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a system of $
The increasing level of experimental control over atomic and optical systems gained in the past years have paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many
We investigate the limits of effectiveness of classical spin simulations for predicting free induction decays (FIDs) measured by solid-state nuclear magnetic resonance (NMR) on systems of quantum nuclear spins. The specific limits considered are asso
Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this