Related papers: Transversal gates for quantum CSS codes

Transversal gates for quantum CSS codes

URL: http://arxiv.org/abs/2601.21514v1
Date: Thu, 29 Jan 2026 10:28:58 GMT
Title: Transversal gates for quantum CSS codes
Authors: Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews, Narayanan Rengaswamy, Rodrigo San-José,
Abstract summary: We focus on the problem of computing the set of diagonal gates fixing a CSS code.<n>We determine the logical actions of the gates as well as the groups of gates that induce non-trivial logical gates and logical identities.
Score: 10.827497136745551
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and logical identities. We explicitly declare the set of equations defining the groups, a key advantage and differentiator of our approach. We compute the complete set of transversal stabilizers and transversal gates for any CSS code arising from monomial codes, a family that includes decreasing monomial codes and polar codes. As a consequence, we recover and extend some results in the literature on CSS-T codes, triorthogonal codes, and divisible codes.

Related papers

Low Overhead Universal Quantum Computation with Triorthogonal Codes [8.516351290711953]
We study the use of triorthogonal codes for universal fault-tolerant quantum computation.<n>We propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both universality and a gate set.
arXiv Detail & Related papers (2025-10-07T09:17:10Z)
Asymptotically good CSS-T codes and a new construction of triorthogonal codes [0.0]
We propose a new systematic construction of CSS-T codes from any given CSS code using a map $phi$.<n>We prove the existence ofally good binary CSS-T codes, and ofally good quantum LDPC CSS-T codes.<n>An immediate application of these codes in dealing with coherent noise is discussed.
arXiv Detail & Related papers (2024-12-11T18:03:58Z)
Targeted Clifford logical gates for hypergraph product codes [54.57204856880369]
We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group.<n>This enables us to design explicit transformations that result in targeted logical gates for arbitrary codes in this family.
arXiv Detail & Related papers (2024-11-26T02:32:44Z)
Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
arXiv Detail & Related papers (2024-10-10T04:07:24Z)
Equivalence Classes of Quantum Error-Correcting Codes [49.436750507696225]
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. We represent QECC's in a form called a ZX diagram, consisting of a tensor network.
arXiv Detail & Related papers (2024-06-17T20:48:43Z)
Graphical CSS Code Transformation Using ZX Calculus [0.6734802552703861]
We present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. We show how ZX and graphical encoder maps relate several equivalent perspectives on these code-transforming operations.
arXiv Detail & Related papers (2023-07-05T17:04:49Z)
Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
arXiv Detail & Related papers (2023-03-24T00:29:15Z)
CSS code surgery as a universal construction [51.63482609748332]
We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes. We describe code surgery between such codes using a specific colimit in the category of chain complexes.
arXiv Detail & Related papers (2023-01-31T16:17:25Z)
Morphing quantum codes [77.34726150561087]
We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate. We construct a family of hybrid color-toric codes by morphing the color code.
arXiv Detail & Related papers (2021-12-02T17:43:00Z)
Designing the Quantum Channels Induced by Diagonal Gates [0.5735035463793007]
Diagonal gates play an important role in implementing a universal set of quantum operations. This paper describes the process of preparing a code state, applying a diagonal physical gate, measuring a code syndrome, and applying a Pauli correction.
arXiv Detail & Related papers (2021-09-28T04:39:15Z)
Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
arXiv Detail & Related papers (2021-08-10T15:00:20Z)
Classical Coding Problem from Transversal $T$ Gates [10.478611957969145]
We show that triorthogonal codes are, essentially, the only family of CSS codes that realize logical $T$ via physical $T$. We also use Ax's theorem to characterize the logical operation realized on a family of quantum Reed-Muller codes.
arXiv Detail & Related papers (2020-01-14T16:45:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.