Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits

Guanyu Zhu, Ali Lavasani, and Maissam Barkeshli
Phys. Rev. Lett. 125, 050502 – Published 28 July 2020
PDFHTMLExport Citation

Abstract

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order of the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the lengths of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, our results demonstrate that a universal logical gate set can be implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead. These results also apply directly to braiding of topological defects in surface codes. Our results reformulate the notion of braiding in general as an effectively instantaneous process, rather than as an adiabatic, slow process.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 14 May 2019
  • Accepted 8 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.050502

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyStatistical Physics & Thermodynamics

Authors & Affiliations

Guanyu Zhu, Ali Lavasani, and Maissam Barkeshli

  • Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 125, Iss. 5 — 31 July 2020

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×