NASA - National Aeronautics and Space Administration

Many-body systems, especially those in solid state physics, present some challenging questions about the nature of entanglement in real materials. While entanglement is quite well-understood and characterised for bipartite systems, when there are more than two components to the particle ensemble very little is known.

We have introduced inequalities for multipartite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found. These inequalities translate directly into spin correlation measurements that could be made in the laboratory.

Physical Review Letters article

Quantum many-body physics plays a dual role in quantum computation. On the one hand, all physical implementations of quantum computers are many-body systems. This aspect is commonly appreciated. A less appreciated yet equally important aspect concerns quantum algorithms. There is a generally acknowledged need to find new quantum algorithms. At present all confirmed polynomial-time quantum algorithms solve one or another version of a hidden subgroup problem, the most celebrated example being the Shor algorithm for integer factoring problem. Quantum many-body physics, with its enormous technical power, can be instrumental in finding new algorithms. In turn, quantum computing has strongly stimulated modern physics and in particular nanotechnology. Making a quantum computer is an enormous challenge that requires new physical ideas and technologies. But once made, a quantum computer will allow studying physical, chemical and biological systems on a level that can never be reached with classical computers.

Crucial for successful implementation of quantum computing is the connection of quantum algorithms and the physical systems that are used for specific computer implementations. Along with initially pictured systems where the interaction between any pair of qubits is turned on and off at will, more and more systems are developed where this possibility does not exist. The future algorithms should take advantage of the architectures closely related to the prospective candidate systems, and in particular the systems where the interqubit coupling cannot be changed once the system is built.

In general, the success of many-body quantum algorithms substantially depends on the details of the strong interaction between quantum spins that represent qubits. For example, one can expect that despite the effects of randomness in the bit-structure of famous NP-complete problems strong interaction may lead to an entangled state with quantum correlations extending out over large groups of spins. Such collective effects are well known in systems with short-range fundamental interactions. Examples include the formation of a spin glass order in random magnets and Aharonov-Bohm effects in fractional quantum Hall systems. The onset of the quantum collective phenomena usually occurs via the phase transitions that are at the root of the complexity analysis of NP-complete problems.

The real test of many-body quantum algorithms is experiment. One way to implement collective many-body effects in quantum computation is to perform experiments where a computational basis is formed by the many-particle superposition states. At the moment, a scalable universal quantum computer (UQC) is not available and it is very important to do experiments with alternative architectures in the macroscopic and mesoscopic systems and to study the \lq\lq analog" quantum computation.

The analysis of typical complexity of quantum algorithms can be viewed as a new branch of mesoscopic physics for strongly correlated quantum many-qubit systems. Also the development of new quantum algorithms and understanding of the role of entanglement in many-body systems will be based on new physical insights, including systems with nonlocal interactions and with direct many-particle interaction, localization by constructed disorder, quantum chaos, quantum phase transitions, ideas from spin glass theory, and topological effects in many-body systems. On the other hand, simulating physical systems and many-body phenomena on a quantum computer will lead to new understanding of the effects of many-body interactions in real systems.

NASA Ames Research Center Organized an International Conference "Quantum Computation and Many-body Systems" with top experts in the field of quantum computing and many-body physics to discuss the future development of the field.