Designer Quantum Materials

Spin-based quantum information processing relies on the ability to identify and coherently manipulate quantum bits (qubits) existing in nature in the form of spin-1/2 particles such as electrons. The work described in this thesis is based on an alternative perspective: that these spin-1/2 objects, together with their interactions, can be regarded as building blocks of a variety of “designer quantum materials” with features not present for isolated single spins. Theoretical proposals are presented for two classes of spin-based designer quantum materials relevant for quantum information transport and manipulation. The first class of materials involves spin-1/2 networks coupled by spatially-varying exchange interactions, in which moving domain walls can produce topologically-stable “flying spin qubits,” and pairs of domain walls can be used to generate and transport Einstein-Podolsky-Rosen pairs of entangled qubits. The effective exchange between two domain-wall qubits can be tuned by adjusting the positions of the domain walls and can be ferromagnetic even when all spin-spin couplings are antiferromagnetic. The second class of designer quantum materials consists of electron spins in quantum wires with spatially-varying spin-orbit coupling. The presence of the spin-orbit interaction introduces pseudo-Zeeman couplings of the electron spins to effective magnetic fields and further enhances the building-block toolset: by periodically modulating this spin-orbit coupling in space, it is possible to create the spatial analogue of spin resonance, without the need for any real magnetic fields. The mapping of time-dependent operations onto a spatial axis suggests a new mode for quantum information processing in which gate operations are encoded into the band structure of the material