Universal quantum computation with ordered spin-chain networks

TL;DR

This paper demonstrates how anisotropic spin chains with ordered ground states can be used for universal quantum computation by implementing a complete set of fault-tolerant quantum gates through controlled spin interactions.

Contribution

It introduces a novel approach to quantum computing using ordered spin-chain networks, bridging traditional and topological quantum computation methods.

Findings

Realization of single-qubit Hadamard, phase, and pi/8 gates.

Implementation of two-qubit CNOT gate.

Some single-qubit operations are geometric, relying on anisotropy control.

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.