A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We find that almost all properties of the Hamiltonian are determined by its surface, and that these properties can be measured even if the system can only be initialised to a mixed state.

The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks.

We prove that the optimal strategy to store an unknown group transformation into a quantum memory is to apply the available uses in parallel on a suitable entangled state. The optimal retrieving strategy is the incoherent, ``measure-and-rotate'' strategy, in which the quantum memory is measured and a unitary depending on the outcome is performed. The same result holds for approximate re-alignment of reference frames for quantum communication.

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. Notably this construction allows for geometric robustness based upon the control of two independent qubit interactions.