Adiabatic topological quantum computing

Abstract

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.

23 pages, 33 figures

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Cited by in corpus (10)

• Poking holes and cutting corners to achieve Clifford gates with the surface code
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Generalized Cluster States Based on Finite Groups
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Superconducting qubit circuit emulation of a vector spin-1/2
• Topological Quantum Gates in Homotopy Type Theory
• Creation and manipulation of surface code defects with quantum optimal control
• Suppression of effective noise in Hamiltonian simulations
• A digital quantum simulator in the presence of a bath