Resources Required for Topological Quantum Factoring

Abstract

We consider a hypothetical topological quantum computer where the qubits are comprised of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313 (2006)] which combines topological and non-topological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128 bit number requires approximately 10^3 Fibonacci anyons versus at least 3 x 10^9 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially.

4+epsilon pages, 4 figures

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Cited by in corpus (9)

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• A Short Introduction to Topological Quantum Computation
• Introduction to topological quantum computation with non-Abelian anyons
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Quantum Circuits for Measuring Levin-Wen Operators
• Parafermion supporting platform based on spin transitions in the fractional quantum Hall effect regime
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
• A Universal Circuit Set Using the $S_3$ Quantum Double