Computers permeate all socio-economic activities of our times. The limitations of our present silicon-based computational power are no longer residing in the far future. The topic of this award is one that is relevant to finding new directions for future computation, while at the same time enlarging our understanding of physical systems suitable for quantum computing. The research will address fundamental science questions, such as whether topological states of matter can store, at non-zero temperatures, quantum (qubit) or classical (bit) elements of information. The research activities will be accompanied by educational efforts at three different levels: The PIs will provide solid education and training to graduate students in the field of quantum information; they will develop undergraduate courses at the interface between physics and computer science; and they will use their expertise to help develop the "Future of Information" module for techCAMP, a program directed towards middle-school and high-school teachers.
Encoding information in topological states of certain many-particle systems has been proposed as robust way to store quantum information. In these systems, the ground state is not unique and its multiplicity is not altered by local perturbations. As a result, when used to encode information, topological qubits are less susceptible to errors than standard qubits. Although protected from static perturbations, it is still uncertain how effective topological quantum memories are in the presence of dynamical perturbations. The proposed research addresses two important aspects of this issue. The first concerns the study of loss of coherence in realistic setups, where both equilibrium and non-equilibrium noise must be considered. The second is whether topological quantum memories in the presence of thermal fluctuations are attainable in physically realizable systems. Building on these investigations, the goal is to find ways to improve fault tolerance in topological quantum information processing.
Computers permeate all socio-economic activities of our times. The limitations of our present silicon-based computational power are no longer residing in the far future. The topic of this award is one that is relevant to finding new directions for future computation, while at the same time enlarging our understanding of physical systems suitable for quantum computing. The research carried under the NSF support analyzed the effects of noise on the robustness of quantum memories build with topological qubits (fundamental elements for storing quantum information). Although protected from quasistatic perturbations, there was uncertainty on how effective topological quantum memories were in the presence of dynamical perturbations. The studies identified sources of errors affecting the qubits in the presence of non-equilibrium noise and identified ways to improve fault tolerance in topological quantum information processing. The need for increasing computational power continues to motivate not only the development of new hardware technologies but also alternative, more efficient algorithms. In this project we used ideas developed in the context of quantum information theory to design more efficient classical algorithms. We developed a new form of parallel computing on classical computers. The method is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs at the same time. The research also explored the connection between the difficulty in reversing "black-box" quantum circuits and the statistical fluctuations of the entanglement spectrum of quantum states. The research activities were accompanied by educational efforts at the graduate and undergraduate levels: The Principal Investigators provided solid education and training to students in the field of quantum computation, and they developed courses at the interface between physics and computer science.
