Geometric Effects and Computation in Spin Networks

Abstract

When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by performing rotations on the spin. Such effects can be used to determine properties of the chain, such as its length, in a robust manner. Alternatively, they can form the basis of a spin network quantum computer. We demonstrate a universal set of gates in such a system by both dynamical and geometrical means.

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• State Transfer and Spin Measurement
• Quantum state transfer and time-dependent disorder in Quantum Chains
• Symmetry & Controllability for Spin Networks with a Single-Node Control
• Directional Coupling for Quantum Computing and Communication
• Nested entangled states for distributed quantum channels
• Superballistic Diffusion of Entanglement in Disordered Spin Chains
• Designing pretty good state transfer via isospectral reductions
• Almost perfect transport of an entangled two-qubit state through a spin chain
• Time Independent Universal Computing with Spin Chains: Quantum Plinko Machine
• Communication in quantum networks of logical bus topology
• Generating Quantum States through Spin Chain Dynamics
• Adiabatic geometric phases in hydrogenlike atoms
• Quantum Control Theory for State Transformations: Dark States and their Enlightenment
• Beam Splitter for Spin Waves in Quantum Spin Network
• Analysis and minimization of bending losses in discrete quantum networks
• Almost perfect transmission of multipartite entanglement through disordered and noisy spin chains
• Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder
• Many-body strategies for multi-qubit gates - quantum control through Krawtchouk chain dynamics
• Quantum dynamics of magnetically controlled network for Bloch electrons
• Robust and efficient transport of two-qubit entanglement via disordered spin chains
• Tailoring Spin Chain Dynamics for Fractional Revivals
• Entanglement creation and distribution on a graph of exchange-coupled qutrits
• Exact generation of quantum states by the dynamics of spin chains
• Entanglement transfer via Chiral Quantum Walk on a Triangular Chain
• Geometric phases in dressed state quantum computation
• Large effects of boundaries on spin amplification in spin chains