Harnessing Symmetry-Protected Topological Orders for Quantum Computation

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Computers have become ubiquitous and indispensable in modern society, and the search for new and more powerful computers is constant. One avenue of exploration is to develop computation based on using quantum information processing (QIP). QIP takes advantage of quantum states, for instance spins of electrons, to encode information. Quantum effects such as "superposition" and "entanglement" enable QIP devices to process information with shades of gray beyond the conventional black-or-white (so-called 0-or-1) logic, and to attain drastic improvements over conventional devices. However, there are two major challenges to achieving the goal of a QIP-based system. One is to find ways to scale up QIP devices, building on recent experiments with small numbers of quantum bits. The other challenge is to discover more examples, and whole categories, of informational tasks for which QIP devices surpass conventional devices. The goal of this project is to address these key issues using ideas from the study of many-body quantum physics phenomena such as superconductivity and magnetism, as, for example, how frustrated quantum spin systems that exhibit exotic magnetism also possess intrinsic capability as a quantum computer. In more general terms, the project will explore ways to use macroscopic quantum order to obtain some quantum advantage in computation and simulation. This research will contribute to the knowledge base of quantum information science and to the training of future scientists in this highly interdisciplinary and rapidly expanding field.The framework of measurement-based quantum computation (MQC) is a convenient way to study the origin of quantum advantages such as quantum speed-up in computation. MQC needs entangled states as a resource. This project will examine how certain types of macroscopic entanglement which are naturally found in quantum spin liquid phases of frustrated quantum spin systems called symmetry-protected topological orders (SPTO) can be used as a resource for MQC. This project will explore how a higher level of entanglement with more intrinsic quantum-gate complexity (Clifford hierarchy) is available by using higher-dimensional SPTO. The new entanglement by 2D SPTO has several features which are not available by conventional universal entanglement (like the cluster state whose SPTO is of a 1D nature), and is in contrast capable of universal quantum computation even by simplest single-spin X, Y, and Z measurements. This project takes advantage of this concrete connection between macroscopic quantum orders and quantum complexity to approach the key issues about scalability and non-classical complexity in quantum computation and simulation. Thus it builds connections between two research fields: quantum information science and quantum many-body physics.