Work

Four-dimensional toric code with non-Clifford transversal gates

Year: 2021

Type: article

Abstract: The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical CCCZ gate transversally.The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyperdiamond.This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical X and Z and only allows for the implementation of a transversal Clifford gate.This paper further develops the established connection between topological dimension and transversal gates in the Clifford hierarchy, generalizing the known designs for the implementation of transversal CZ and CCZ in two and three dimensions, respectively.

Source: Physical Review Research

DOI: 10.1103/physrevresearch.3.013118

Authors: Tomas Jochym-O'Connor, Theodore J. Yoder

Institutions: IBM (United States), IBM Research - Thomas J. Watson Research Center

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: International Business Machines Corporation