Resources Required for Topological Quantum Factoring

TL;DR

This paper estimates the qubit resources needed for topological quantum computers using Ising and Fibonacci anyons to run Shor's algorithm, highlighting significant resource differences.

Contribution

It provides a comparative analysis of resource requirements for topological quantum factoring with different anyon types and distillation methods.

Findings

Fibonacci anyons require about 10^3 qubits for 128-bit factoring.

Ising anyons need at least 3 x 10^9 qubits under current methods.

Alternative distillation algorithms could reduce Ising anyon resource needs.

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.