Southwest Quantum Information and Technology

Thresholds for universal concatenated quantum codes

Presenting Author: Tomas Jochym-O'Connor, California Institute of Technology
Contributing Author(s): Christopher Chamberland (IQC, University of Waterloo), Raymond Laflamme (IQC, University of Waterloo, Perimeter Institute)

Quantum computing algorithms will require fault-tolerance in order to suppress errors to sufficiently small levels for growing algorithmic complexity. Possible fault-tolerant implementations are far-ranging, all requiring qubit and computational resource overheads. Moreover, the level of precision required to implement a computation fault-tolerantly can differ greatly depending on the type of implementation used. In practice, the choice of fault-tolerant architecture will likely depend on the physical qubit architecture and the particular algorithm that is desired to be implemented, and as such it is of particular importance to understand the parameters at which fault-tolerant computation becomes possible for different proposals. The surface code is the leading contender for a fault-tolerant architecture due to the low weight of its stabilizer generators as well as its high fault-tolerance threshold rate, the physical error rate below which errors can be suppressed in an exponential manner. However, in order to complete a universal gate set for quantum computation, the surface code requires the preparation of a special ancillary state, a magic state. As such, to prepare a magic state with high fidelity, a process called magic state distillation is used, leading to high offline qubit overhead. In order to circumvent the need for magic state distillation, recent research efforts in quantum error correction have focused on finding alternative methods to implementing universal fault-tolerant gate sets. The first step towards determining whether these alternative methods will provide potential improvements over the surface code is to consider their fault-tolerance threshold. In this work, we present an upper bound on the asymptotic threshold for a concatenated scheme for universal fault-tolerant computation without magic state distillation. We show that the upper bound on the asymptotic threshold of \(1.28~\times~10^{-3}\) is competitive with other concatenated schemes, such as the Golay code.

Read this article online: https://arxiv.org/abs/1603.02704

(Session 5 : Thursday from 5:00pm - 7:00pm)