Quantum Concatenated Code Hamiltonians

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As the basic building blocks of computers shrink to the atomic scale, new physics, in particular quantum physics, arises which shapes how these devices function. Systems that could previously robustly store information, when they are scaled down to atomic scales, lose their ability to robustly store information. On the other hand, it is known that if one could build computers at atomic scales which operate strictly according to the laws of quantum physics, then these computers would offer significant advantages overtoday?s classical computers. Quantum computers, if they could be built, would break today?s modern cryptosystems and revolutionize the simulation of quantum many-body physics. The research proposed here would result in a new method for constructing robust devices for storing and manipulating quantum information. This method starts with the observation that classical information storage is made possible by the physics of the devices used to store the information. For example, the magnetic domains used to store information on a hard drive are robust storage devices exactly because of the existence of an ordered low temperature phase in the Ising model (in two or greater dimensions.) The research described here follows the same principles which allow robust classical storage of information: in short the research attempts to show how toengineer condensed matter systems which can act as a quantum hard drive. Thisresearch is particulary novel in that it makes direct contact with the traditional method for showing that robust quantum computation is possible, concatenated coding. In standard error correction, encoding information across multiple independently erred systems reduces the rate that information is destroyed. By encoding encoded information, also known as concatenating, one can achieve an even further reduction in the rate of information destruction. In this research this is put to use in constructing a particular class of many-body quantum system, called quantum concatenated code Hamiltonians, which use the concatenation idea on energy landscapes to preserve quantum information. The research includes a theoretical study validating the robust storage capability of concatenated code Hamiltonians along a plan for implementing themodel in a variety of realistic architectures. The final outcome of the research will be the schematics for a new type of quantum information storage device, one which will drastically improve the prospects for building a quantum computer.