Universal quantum computation with ordered spin-chain networks

Abstract

It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and pi/8 gates as well as the two-qubit CNOT gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of p-wave superconducting wires discussed in the literature.

9 pages, 3 figures

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• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Majorana edge states in interacting one-dimensional systems
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• Universal quantum computation on a semiconductor quantum wire network
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• Spin-orbit mediated anisotropic spin interaction in interacting electron systems

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• Gate control of Berry phase in III-V semiconductor quantum dots
• Majorana end states in an interacting quantum wire
• Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders
• Theory of topological spin Josephson junctions
• High-temperature quantum coherence of spinons in a rare-earth spin chain
• The Simulation of Non-Abelian Statistics of Majorana Fermions in Ising Chain with Z2 Symmetry
• Quantum spin chains and random matrix theory
• A witness for topological order and stable quantum memories in abelian anyonic systems
• Encoding a qubit with Majorana modes in superconducting circuits
• Universal quantum operation of spin-3/2 Blume-Capel chains