[quantum-info] PIQuDos seminar Wed Sept 24: Beni Yoshida

[Gus Gutoski]

Reminder of PIQuDos seminar today by Beni Yoshida.  -Gus

On Fri, Sep 19, 2014 at 4:37 PM, Gus Gutoski <ggutoski at perimeterinstitute.ca
> wrote:

> Please join us on Wednesday, September 24 at 4pm in the Time room for
> a quantum information seminar by Beni Yoshida.
>
> Title:  Fault-tolerant logical gates in quantum error-correcting codes
> Speaker: Beni Yoshida (Caltech)
>
> Abstract: Recently, Bravyi and Koenig have shown that there is a
> tradeoff between fault-tolerantly implementable logical gates and
> geometric locality of stabilizer codes. They consider
> locality-preserving operations which are implemented by a constant
> depth geometrically local circuit and are thus fault-tolerant by
> construction. In particular, they shown that, for local stabilizer
> codes in D spatial dimensions, locality preserving gates are
> restricted to a set of unitary gates known as the D-th level of the
> Clifford hierarchy. In this paper, we elaborate this idea and provide
> several extensions and applications of their characterization in
> various directions. First, we present a new no-go theorem for
> self-correcting quantum memory. Namely, we prove that a
> three-dimensional stabilizer Hamiltonian with a locality-preserving
> implementation of a non-Clifford gate cannot have a macroscopic energy
> barrier. Second, we prove that the code distance of a D-dimensional
> local stabilizer code with non-trivial locality-preserving m-th level
> Clifford logical gate is upper bounded by L^{D+1-m}. For codes with
> non-Clifford gates (m>2), this improves the previous best bound by
> Bravyi and Terhal. Third we prove that a qubit loss threshold of codes
> with non-trivial transversal m-th level Clifford logical gate is upper
> bounded by 1/m. As such, no family of fault-tolerant codes with
> transversal gates in increasing level of the Clifford hierarchy may
> exist. This result applies to arbitrary stabilizer and subsystem
> codes, and is not restricted to geometrically-local codes. Fourth we
> extend the result of Bravyi and Koenig to subsystem codes. A technical
> difficulty is that, unlike stabilizer codes, the so-called union lemma
> does not apply to subsystem codes. This problem is avoided by assuming
> the presence of error threshold in a subsystem code, and the same
> conclusion as Bravyi-Koenig is recovered.
>
> This is a joint work with Fernando Pastawski.
> arXiv:1408.1720
>
> Date: Wednesday, September 24, 2014.
> Time: 16:00
> Location: Time Room
>
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