CENTER FOR EXOTIC QUANTUM SYSTEMS CEQS Preskill 1983 Kitaev 2002 Refael 2005 Motrunich 2006 Fisher 2009 Historically, Caltech physics has focused on the most “fundamental” problems, such as the structure of matter at the smallest conceivable scales, and the structure of the universe at the largest conceivable scales. These problems are still enormously exciting, but there is also another frontier, just as exciting and important, which might be called the “entanglement frontier.” Research in this area aims to understand and exploit the exotic and baffling correlations exhibited by quantum systems. State-of-the-art experiments can be done on a tabletop, and there are very strong ties between experiment and theory.

CENTER FOR EXOTIC QUANTUM SYSTEMS CEQS In the 21 st century, building strength in quantum many-body theory has been a high priority for Caltech physics, and we have been quite successful. Furthermore, links to the theory of computation and to atomic-molecular- optical physics make this research highly interdisciplinary, something Caltech does especially well. A central theme: seeking new paradigms for describing universal emergent phenomena in quantum systems containing many particles. We need new ideas to erect a “grand unified theory” of exotic quantum systems! Preskill 1983 Kitaev 2002 Refael 2005 Motrunich 2006 Fisher 2009

Quantum Entanglement classically correlated socksquantumly correlated photons There is just one way to look at a classical bit (like the color of my sock), but there are complementary ways to observe a quantum bit (like the polarization of a single photon). Thus correlations among qubits are richer and much more interesting than correlations among classical bits. A quantum system with two parts is entangled when its joint state is more definite and less random than the state of each part by itself. Looking at the parts one at a time, you can learn everything about a pair of socks, but not about a pair of qubits!

The quantum correlations of many entangled qubits cannot be easily described in terms of ordinary classical information. To give a complete classical description of one typical (highly entangled) state of just a few hundred qubits would require more bits than the number of atoms in the visible universe! It will never be possible, even in principle to write down such a description.

We can’t even hope to describe the state of a few hundred qubits in terms of classical bits. That’s why highly correlated quantum systems can behave in ways that we find hard to understand. But it also means that controlling highly entangled systems might be very powerful. As Feynman first suggested in 1981, a computer that operates on qubits rather than bits (a quantum computer) should be able to perform tasks that are beyond the capability of any conceivable digital computer!

( + ) Decoherence Environment ( + )

Decoherence Environment ( + ) Decoherence explains why quantum phenomena, though observable in the microscopic systems studied in the physics lab, are not manifest in the macroscopic physical systems that we encounter in our ordinary experience.

Quantum Computer Environment Decoherence ERROR! How can we protect a quantum system from decoherence and other sources of error?

CENTER FOR EXOTIC QUANTUM SYSTEMS CEQS Why Fellowships? In theory as in experiment, students and postdocs make an essential contribution to the research effort. That’s particularly true when it comes to exploiting interdisciplinary opportunities and fast-breaking developments. Students and postdocs can provide the glue that binds different research groups together, and often they lead the faculty into new territory rather than the other way around. Gottesman: Quantum error- correcting codes Smith: Quantum channel capacities Bonderson: Experimental signature of nonabelian statistics. Chang: Entangling mechanical oscillators Bacon: Self- correcting systems Verstraete: Complexity of quantum problems

Vidal Efficient classical simulation of quantum systems with bounded entanglement In general, there is no succinct classical description of the quantum state of a system of n qubits. But suppose, e.g., for qubits arranged in one dimension, that for any way of dividing the line into two segments, the strength of the quantum correlation (the amount of entanglement) between the two parts is bounded above by a constant, independent of n. Vidal showed that in that case a succinct description is possible, with O( n ) parameters rather than 2 n, and that the description can be easily updated as the state evolves (if the interactions are local). This makes precise the idea that entanglement is the source of a quantum computer’s power: if the quantum computer does not become highly entangled, it can be efficiently simulated by a classical computer. Furthermore, in one-dimensional systems with local interactions, the entanglement increases no more rapidly than log n, and an efficient classical simulation of real time evolution is possible.

Universal properties of entanglement For the ground state of a large two-dimensional quantum system, consider the entanglement of a disk (circumference L) with the rest of the system. For a system with a nonzero energy gap, the entanglement is: L The universal additive term, the topological entanglement entropy, is a global feature of the many-body quantum entanglement, characterizing the topological order of the gapped two-dimensional system. There is a simple formula for the universal constant , in terms of the properties of the particle excitations of the system. PreskillKitaev Term proportional to L, arising from short distance fluctuations near the boundary, is nonuniversal. Additive correction is universal (independent of geometry and microscopic details).

Quantum Information Science Atomic-Molecular Optical Physics Condensed Matter Physics CEQS!