A Blueprint for a Topologically Fault-tolerant Quantum Computer

Abstract

The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical" computer, including any potential non-quantum technologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantum computer. The topological approach to quantum computation proposes to surmount this obstacle by using special physical systems -- non-Abelian topologically ordered phases of matter -- that would provide intrinsic fault-tolerance at the hardware level. The so-called "Ising-type" non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantum computation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing these operations were unknown. Here we show how the necessary operations can be physically implemented for Ising-type systems realized in the recently proposed superconductor-semiconductor and superconductor-topological insulator heterostructures. Furthermore, we specify routines employing these methods to generate a computationally universal gate set. We are consequently able to provide a schematic blueprint for a fully topologically-protected Ising based quantum computer using currently available materials and techniques. This may serve as a starting point for attempts to construct a fault-tolerant quantum computer, which will have applications to cryptanalysis, drug design, efficient simulation of quantum many-body systems, solution of large systems of linear equations, searching large databases, engineering future quantum computers, and -- most importantly -- those applications which no one in our classical era has the prescience to foresee.

6 pages, 5 figures

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Cited by in corpus (9)

• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• A new platform for topological quantum phenomena : Topological Insulator states in thermoelectric Heusler-related ternary compounds
• Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit
• Majorana Fermion Codes
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
• The search for strong topological insulators
• Local realizations of anyon exchange symmetries without lattice dislocations
• Twisted Interferometry
• Twisted Interferometry: the topological perspective