Transversal Diagonal Logical Operators for Stabiliser Codes
- URL: http://arxiv.org/abs/2303.15615v2
- Date: Wed, 26 Apr 2023 10:22:37 GMT
- Title: Transversal Diagonal Logical Operators for Stabiliser Codes
- Authors: Mark A. Webster, Armanda O. Quintavalle, and Stephen D. Bartlett
- Abstract summary: Pauli group operators can be implemented on quantum error correction codes.
We identify logical operators composed of single and multi-qubit diagonal Clifford hierarchy gates.
We show a method for constructing CSS codes that have a desired diagonal logical Clifford hierarchy operator implemented using single qubit phase gates.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Storing quantum information in a quantum error correction code can protect it
from errors, but the ability to transform the stored quantum information in a
fault tolerant way is equally important. Logical Pauli group operators can be
implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category
of codes, by applying a series of physical Pauli X and Z gates. Logical
operators of this form are fault-tolerant because each qubit is acted upon by
at most one gate, limiting the spread of errors, and are referred to as
transversal logical operators. Identifying transversal logical operators
outside the Pauli group is less well understood. Pauli operators are the first
level of the Clifford hierarchy which is deeply connected to fault-tolerance
and universality. In this work, we study transversal logical operators composed
of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate
algorithms for identifying all transversal diagonal logical operators on a CSS
code that are more general or have lower computational complexity than previous
methods. We also show a method for constructing CSS codes that have a desired
diagonal logical Clifford hierarchy operator implemented using single qubit
phase gates. Our methods rely on representing operators composed of diagonal
Clifford hierarchy gates as diagonal XP operators and this technique may have
broader applications.
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