Quantum simulators permit the study of quantum systems that are difficult to study in the laboratory and impossible to model with a supercomputer. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems.
A universal quantum simulator is a quantum computer proposed by Richard Feynman in 1982. Feynman showed that a classical Turing machine would experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch in 1985, took the ideas further and described a universal quantum computer. In 1996, Seth Lloyd showed that a standard quantum computer can be programmed to simulate any local quantum system efficiently.
A quantum system of many particles is described by a Hilbert space whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system. As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems.
Quantum simulators have been realized on a number of experimental platforms, including systems of ultracold quantum gases, trapped ions, photonic systems and superconducting circuits. 
A trapped-ion simulator, built by a team that included the NIST and reported in April 2012, can engineer and control interactions among hundreds of quantum bits (qubits). Previous endeavors were unable to go beyond 30 quantum bits. As described in the scientific journal Nature, the capability of this simulator is 10 times more than previous devices. Also, it has passed a series of important benchmarking tests that indicate a capability to solve problems in material science that are impossible to model on conventional computers.
Furthermore, many important problems in physics, especially low-temperature physics, remain poorly understood because the underlying quantum mechanics is vastly complex. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles. Better computational tools are needed to understand and rationally design materials, such as high-temperature superconductors, whose properties are believed to depend on the collective quantum behavior of hundreds of particles.
The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of beryllium ions, less than 1 millimeter in diameter, hovering inside a device called a Penning trap. The outermost electron of each ion acts as a tiny quantum magnet and is used as a qubit, the quantum equivalent of a "1" or a "0" in a conventional computer. In the benchmarking experiment, physicists used laser beams to cool the ions to near absolute zero. Carefully timed microwave and laser pulses then caused the qubits to interact, mimicking the quantum behavior of materials otherwise very difficult to study in the laboratory. Although the two systems may outwardly appear dissimilar, their behavior is engineered to be mathematically identical. In this way, simulators allow researchers to vary parameters that couldn't be changed in natural solids, such as atomic lattice spacing and geometry.
Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states . Kim et al., extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between frustration and entanglement  and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a phase transition between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9 . Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir  and Lanyon et al. demonstrated digital quantum simulation with up to 6 ions. Islam, et al., demonstrated adiabatic quantum simulation of the transverse Ising model with variable (long) range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the antiferromagnetic interaction range . Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism.
Simulators exploit a property of quantum mechanics called superposition, wherein a quantum particle is made to be in two distinct states at the same time, for example, aligned and anti-aligned with an external magnetic field. So the number of states simultaneously available to 3 qubits, for example, is 8 and this number grows exponentially with the number of qubits: 2N states for N qubits.
Crucially, the simulator can also engineer a second quantum property called entanglement between the qubits, so that even physically well separated particles may be made tightly interconnected.