  A quantum simulator is a restricted class of quantum computer that controls
the interactions between quantum bits in a way that can be mapped to certain
difficult quantum many-body problems. As more control is exerted over larger
numbers of qubits, the simulator can tackle a wider range of problems, with the
ultimate limit being a universal quantum computer that can solve general
classes of hard problems. We use a quantum simulator composed of up to 53
qubits to study a non-equilibrium phase transition in the transverse field
Ising model of magnetism, in a regime where conventional statistical mechanics
does not apply. The qubits are represented by trapped ion spins that can be
prepared in a variety of initial pure states. We apply a global long-range
Ising interaction with controllable strength and range, and measure each
individual qubit with near 99% efficiency. This allows the single-shot
measurement of arbitrary many-body correlations for the direct probing of the
dynamical phase transition and the uncovering of computationally intractable
features that rely on the long-range interactions and high connectivity between
the qubits.
