Quantum computation utilizes the counterintuitive behavior of quantum mechanics to achieve a speedup in computational power. Instead of the traditional bit values (0's and 1's) of digital computers, a quantum computer utilizes superpositions of these values, allowing it to occupy multiple different computational states at once. Quantum computers use this "quantum parallelism" to perform such computational tasks as searching large databases, designing new medical drugs, and deciphering cryptographic codes at a speed unmatched by ordinary digital computers.
Despite the phenomenal progress of the last two decades, much work remains before a realistic quantum computer can be built. Scaling up our current experimental setups to larger sizes is a major challenge. The superpositions which give quantum computers their characteristic power are fragile to interactions with the surrounding environment. A great deal of effort has been spent developing scalable hardware and control schemes which isolate quantum computers from these effects. Clever theoretical innovations, such as effective usage of many-body phenomena and methods of quantum error correction, also hold great promise for unlocking the tremendous potential of quantum computation, leading many researchers to believe that quantum computers will become an everyday reality in the not-too-distant future.
Many-body physics is the study of systems composed of many interacting particles. While the problems of many-body physics - especially those pertaining to quantum systems - have historically been regarded as difficult to solve, the development of new theoretical tools in the last thirty years has led to an explosion in our understanding of the general behavior of many-body systems. This has in turn contributed to the discovery and characterization of entirely new many-body phenomena, such as exotic "quantum phases" of matter, whose very existence relies upon the laws of quantum mechanics.
Increasingly, researchers in different areas of physics have realized that strong connections exist between quantum many-body physics and the study of quantum computation. On one hand, quantum computers, themselves being large interacting quantum systems, hold great promise for analyzing the behavior of those many-body systems which have traditionally resisted analysis. On the other, several varieties of quantum many-body systems have been shown to be excellent architectures for quantum computation. Because many commonly-studied quantum many-body systems occur in nature, a means of carrying out quantum computation with such systems would allow nature to do much of the work in constructing a quantum computer, putting us in a good position for achieving practically useful quantum computation.
When quantum computing comes to the fore, its "killer app" will likely be the ability of quantum computers to simulate other quantum systems. As quantum effects are ubiquitous in nature, universal quantum simulation would have applications in quantum physics, quantum chemistry, biology, and even such areas of classical physics as cosmology, making it an attractive goal. It was this prospect that originally motivated Feynman to propose the idea of performing computation with quantum systems in the early eighties. A generic quantum state naively requires exponentially many complex amplitudes to describe it, and so a classical computer cannot even store the description of such a state efficiently, let alone simulate its evolution in time. This exponential tractability gap is only bridged when one considers simulating a quantum system on a computer composed of quantum elements.
Is universal quantum computation truly necessary for this purpose? Today, many researchers are turning to the analog construction of quantum simulators. These devices are not universal but specifically tailored to mimic a small variety of other quantum systems. Progress in this direction has come in the form of ion traps, atoms and molecules trapped in optical lattices, superconducting qubits, and so on. However, many challenges remain as well, the foremost being scaling these systems up in the face of error propagation. As the complexity of encoded information grows, so does that of its errors. It is therefore important to address the question of whether or not quantum simulators are feasible without relying on established quantum error correction techniques. Consequently, the challenge of quantum simulation unifies many seemingly-disparate subfields of quantum computation and is a powerful driving force behind the field today.
From its humble origin as a means of characterizing the performance of steam engines in the mid-19th century, thermodynamics has developed into a pillar of 21st-century physics. Most strikingly, it is a meta-theory, independent of the underlying microscopic physical details which govern it. It is even difficult to imagine a universe where thermodynamics does not hold, where conservation of energy is routinely violated, and shattered teacups regularly reassemble themselves, tea and all, into whole pieces on the countertop.
Contrast thermodynamics with the strangeness of quantum mechanics, and an interesting puzzle emerges. Anti-thermodynamic events are commonplace in the quantum world; systems can deviate from energy-conserving behavior by quantum fluctuations, and time evolution is fully reversible. Thermodynamics must be truly fundamental that it can emerge from an underlying physical theory in which it is nowhere manifest. Several questions immediately come to mind: where does the boundary between the quantum mechanical and the classical, thermodynamic world live, and can we exploit the physics at this boundary to suit our own purposes? Furthermore, what are the implications for quantum computation? It is clear that much exploration is still needed, with many exciting discoveries yet to come.