Holonomic quantum computing in symmetry-protected ground states of spin chains

Abstract

While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetry-protected degenerate ground states of spin-1 chains, while quantum gates are performed by adiabatic non-Abelian holonomies using only single-site fields and nearest-neighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetry-protected ground states.

19 pages, 4 figures. v2: published version

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Cited by in corpus (15)

• Geometric phases in quantum information
• Symmetry protected topological order at nonzero temperature
• Focus on Quantum Memories
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Symmetry-protected self-correcting quantum memories
• Anomalies and entanglement renormalization
• Local characterization of 1d topologically ordered states
• Adiabatic topological quantum computing
• Adiabatic Quantum Transistors
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Realization of a holonomic quantum computer in a chain of three-level systems
• Symmetry-protected adiabatic quantum transistors
• Scalable universal holonomic quantum computation realized with an adiabatic quantum data bus and potential implementation using superconducting flux qubits
• Robust symmetry-protected metrology with the Haldane phase